Rumflfiflhwwl 8... rufisiumwfimi n at. x .. u 3%? 6.5%me v.2 3pm... 3 n3 1...: 3!]. 1.21! .l. 4.86% 3.. in 1. 61.19“ . fins .19.. . ,.i.r.n.aur£.c :5 3.1.3:. .. «he. , u l wavy}? a». u!.¢\.M.vI-ani ‘zwd... .3. x. a. flan. 3 , . . - . . 2i‘zfu".%i‘ 1:: . Juan 38.3-3 hail...» V'Ia “(JIM o\ l Iui I? 1|:fi - f e... 1....) 6133.141!!! ‘5. LIBRARY "NES‘S . . ' 2. Michigan State mg i University This is to certify that the dissertation entitled Model-Based Control of EIectro-Pneumatic Intake and Exhaust Valve Actuators for IC Engines presented by Jia Ma has been accepted towards fulfillment of the requirements for the Ph. D. degree in Mechanical Engineering T ' Major P ss’or‘s Signature 2. / J (‘f‘ Date MSU is an affirmative-action, equal-opportunity employer --'- .I-'-'-t-I-o-a—.-v-I-0---o-.-o-.-p-o-q-O-o-l-c-o-I-O-O-l-e-o- PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 5/08 K:IProj/Acc&Pres/ClRC/DateDuelndd MODEL-BASED CONTROL OF ELECTRO-PNEUMATIC INTAKE AND EXHAUST VALVE ACTUATORS FOR IC ENGINES By Jia Ma A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Mechanical Engineering 2008 ABSTRACT MODEL—BASED CONTROL OF ELECTRO-PNEUMATIC INTAKE AND EXHAUST VALVE ACTUATORS FOR IC ENGINES By J ia Ma Variable valve actuation of Internal Combustion (1C) engines is capable of significantly improving their performance. Variable valve actuation can be divided into two main cat- egories: variable valve timing with cam shaft(s) and camless valve actuation. For cam- less valve actuation, research has been centered in electro-magnetic, electro-hydraulic, and electro—pneumatic valve actuators. This research addresses the detailed modeling and con- trol of a novel electronically controlled, pneumatic-hydraulic valve actuator (EPVA) for both the intake and exhaust valves of an IC engine. The valve actuator’s main function is to provide variable valve timing, lift and duration of the intake and exhaust valves of an IC engine. A system dynamics analysis is provided and followed by a mathematical model. This modeling approach uses Newton’s law, mass conservation and thermodynamic prin- ciples. A control oriented model was developed to reduce computational throughput for real-time model-based control implementation. Simulated model responses were found to be in satisfactory agreement with experimental results. For intake valves, an on-line model reference adaptive system identification technique was employed to estimate system param- eters required for closed-100p adaptive control; and an adaptive valve lift control strategy was developed to reduce both transient and steady-state lift tracking error. Unlike the intake valves, the exhaust valve opens against an in-cylinder pressure that is a function of the engine operational conditions with cycle-to-cycle combustion variations. This pressure disturbance slows down the valve actuator response and increases the variation of valve lift and opening delay. The developed control strategy utilizes model based predictive tech- niques to overcome the randomly varying in-cylinder pressure against. which the exhaust valve opens. Both intake and exhaust valve control strategies were performed on a Ford 5.4 liter 3-valve V8 engine head at different operating conditions. Experimental results were used to validate the control strategies. To My Parents iv ACKNOWLEDGMENTS First, I thank my advisor Dr. Harold Schock for his continuous support of the Ph.D. program. Dr. Schock was always there to listen and to give advices. Four years ago, he had the foresight to initiate the actuator control project, a topic of great importance today. He provided me great opportunities to work independently and to meet my ever expanding experimental equipment requirements as well as to collaborate with a well trained and intelligent team. He taught me how to express my ideas and gave me plenty of room to experiment on them. He always had confidence in me even when I was frustrated. He showed me the need to be persistent to reach any goal. His efforts made the Automotive Research Experiment Station (ARES) at Michigan State University my wonderful research home for the past three and a half years. Special thanks go to my co-advisor, Dr. Guoming Zhu, who is most responsible for helping me complete the writing of this dissertation as well as the challenging research that lies behind it. Dr. Zhu has been a friend and mentor. He taught me how to write academic papers and how to approach research problems in different ways. He brought out the good ideas in me and made me a better engineering researcher. He showed tremendous patience in helping building and debugging the control system hardware. He was always there to meet and discuss my ideas, to proofread and markup my papers and chapters, and to ask me challenging questions to help me think through my problems. Without his encouragement and constant guidance, I could not have finished this dissertation. I also thank the research associates and graduate students at ARES, MSU for their generous help to my work whenever it was needed. Thanks to Tom Stuecken for bright ideas and suggestions regarding how to modify the mechanical experimental setups, as well as machining and installing the mechanical system. Thanks to Andy Fedewa and Joshua Bedford for participating in a number of important discussions and assisting me in the experiments. Thanks to Mulyanto Poort for the aid in the C programming and Andrew Hartsig for performing the WAVETM simulation of the engine. Thanks to David Hung with Visteon COOperation for his extensive contribution to this project and wholehearted support to my career. Their support and effort made it viable for me to complete this work. Let me also say ’thank you’ to Edward Timm, Andreas Petrou Panayi, Kimberly Sarbo and Melissa Jopke at ARES for being delightful colleagues who made the work environment more pleasant and fun. Besides my advisors and co-workers, I would like to thank the rest of my thesis commit- tee: Dr. Ranjan Mukherjee, Dr. Brian Feeney and Dr. Hassan Khalil who asked me good questions, gave insightful comments, reviewed my work and accommodated on the defense time on a short notice. My additional appreciation goes to Dr. Feeney who believed in me and supported me through the good and bad times in my Ph.D. program. During the course of this research work at ARES, MSU (2004 - 2007), I was supported by the US. Department of Energy, National Energy Technology Laboratory, Energy Efficiency and Renewable Energy Division. I want to express my gratitude toward them for sponsoring the project and to Samuel Taylor, the project manager, for his project management and encouragement. Last, but not least, I thank my mother, Rongzhu Gu, and father, Yiwei Ma, for giving me life in the first place, for educating me with aspects from both arts and sciences, for unconditional support and encouragement to pursue my career interests, even when the interests went beyond boundaries of language, field and geography, and for everlasting faith in me. vi TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES 1 Introduction 2 3 1.1 Motivation and Literature Review ....................... 1.2 Scope of Work and Content of Thesis ..................... Mathematical Modeling 2.1 Introduction ................................... 2.2 System Dynamics ................................ 2.2.1 Air Charging Stage ........................... 2.2.2 Expansion and Dwell Stage ...................... 2.2.3 Air Discharging Stage ......................... 2.3 Mathematical Modeling ............................ 2.3.1 Actuator Piston ............................. 2.3.2 Hydraulic Latch/ Damper ........................ 2.3.3 Inlet Port Valve ............................. 2.3.4 Outlet Port Valve ............................ 2.3.5 Spool Valve ............................... 2.3.6 Solenoid ................................. 2.4 Simulations and Experiments ......................... 2.4.1 Experimental Setup ........................... 2.4.2 Simulation ................................ 2.5 Conclusions ................................... Intake Valve Control System Development 3.1 Introduction ................................... 3.2 Level Two Model ................................ 3.2.1 Review of System Dynamics ...................... 3.2.2 Level Two System Modeling ...................... 3.2.3 Level Two Model Validation ...................... 3.3 Control Strategy ................................ 3.3.1 Parameter Definition .......................... 3.3.2 Adaptive Parameter Identification ................... 3.3.3 Closed-Loop Control Scheme ...................... 3.4 Verification of Parameter Identification Convergence on Test Bench 3.4.1 Intake Valve Control System Hardware Configuration ........ 3.4.2 Intake Valve Actuator Driving Circuit ................ vii ix oar—al-i (DOG-\IODQC} 10 11 16 19 20 23 23 24 24 25 27 42 42 42 43 45 47 48 49 51 54 60 60 62 3.4.3 Evaluation of Parameter Identification Convergence ......... 3.5 Closed-loop Intake Valve Control Scheme for Real Time Application . . . . 3.5.1 Closed-loop Lift Control ........................ 3.6 Conclusion .................................... 4 Exhaust Valve Control System Development 4.1 Introduction ................................... 4.2 Exhaust Valve Dynamic Model ........................ 4.2.1 Actuator Model . . . . . . . . . .................... 4.2.2 In-cylinder Pressure Model ....................... 4.2.3 Validation of In—cylinder Pressure Model by Simulation ....... 4.3 Control Strategy ................................ 4.3.1 Peak Displacement Calculation (PDC) ................ 4.3.2 Model Based Initial Condition Prediction (ICP) ........... 4.3.3 Kalman Filter State Estimation (KFE) ................ 4.3.4 Closed—Loop Control Scheme ...................... 4.4 Simulation Result ................................ 4.4.1 Simulation of Peak Displacement Calculation ............ 4.4.2 Simulation of Model Based Initial Condition Prediction ....... 4.4.3 Simulation of Kalman Filter State Estimation ............ 4.4.4 Simulation of Closed-Loop Exhaust Valve Lift Tracking ....... 4.5 Real Time Exhaust Valve Lift Control Algorithm .............. 4.6 Conclusion .................................... 5 Experiment Implementation 5.1 Introduction ................................... 5.2 Experiment Setup ................................ 5.2.1 Mechanical System Configuration ................... 5.2.2 Control System Hardware Configuration ............... 5.2.3 Valve Actuator Driving Circuit .................... 5.3 Experimental Evaluation on Intake Valve Lift Control System ....... 5.3.1 Statistical analysis of Open-loop Valve Bench Data ......... 5.3.2 Closed-loop Valve Lift Control Experimental Responses ....... 5.3.3 Experimental Results at High Engine Speed ............. 5.3.4 Concluding Remarks On Intake Valve Lift Control System ..... 5.4 Experimental Evaluation on Exhaust Valve Lift Control System ...... 5.4.1 Experimental Results of Closed-Loop Exhaust Valve Lift Tracking . 5.4.2 Concluding Remarks On Exhaust Valve Lift Control System . . . BIBLIOGRAPHY viii 62 63 63 73 75 75 75 78 82 83 85 88 95 98 99 100 100 100 104 107 108 110 114 114 114 114 115 118 119 119 126 131 141 143 143 144 150 LIST OF TABLES 2.1 The Experiment Matrix at 30psi ................................................................................ 26 2.2 The Experiment Matrix at 40psi21 ............................................................................ 26 5.1 Statistical study of open-loop valve actuation data with 9mm target lift at 1200rpm ................................................................................................. 125 5.2 Statistical study of open-loop valve actuation data with 9mm target lift at SOOOrpm ................................................................................................. 126 5.3 Statistical study of open-loop valve actuation data with 3mm target lifi at 1200rpm ................................................................................................. 128 5.4 Maximum SS absolute valve lift error (1200rpm) ..................................................... 131 5.5 Statistical study of closed-loop valve actuation data at 1200rpm .............................. 132 5.6 Maximum SS absolute valve lift error (SOOOrpm). .. ................................................. 142 5.7 Statistical study of closed-loop valve actuation data at SOOOrpm ............................. 144 LIST OF FIGURES 2.1 System dynamics at the air charging stage ................................................................... 7 2.2 System dynamics at the expansion and dwell stage ...................................................... 8 2.3 System dynamics at the air discharging stage ............................................................. 10 2.4 Actuator piston model ................................................................................................. 29 2.5 Hydraulic latch/damper model ................................................................................... 30 2.6 Valve lift profile with the solenoid action chart ........................................................ 31 2.7 Inlet port valve model ................................................................................................ 32 2.8 Outlet port valve model ............................................................................................. 32 2.9 Spool valve model ...................................................................................................... 33 2.10 Solenoid model ........................................................................................................ 33 2.11 Experimental setup ................................................................................................... 34 2.12 Simulation and experiment responses; 30psi pressure supply; lOOms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids .................................................................................................. 35 2.13 Simulation and experiment responses; 30psi pressure supply; 40ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids ......... 36 2.14 Simulation and experiment responses; 30psi pressure supply 24ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids ......... 37 2.15 Simulation and experiment responses; 40psi pressure supply; IOOms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids ................................................................................................... 38 2.16 Simulation and experiment responses; 40psi pressure supply; 40ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids ............ 39 2.17 Simulation and experiment responses; 40psi pressure supply; 24ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids ............ 40 2.18 Simulation and experiment responses; 40psi pressure supply; 100ms solenoid period; 25% solenoid duty cycle; 5ms and 3ms time delay between two solenoids ................................................................................................... 41 2.19 Simulation and experiment responses; 40psi pressure supply; 40ms solenoid period; 25% solenoid duty cycle; 5ms and 3ms time delay between two solenoids ............ 42 2.20 Simulation and experiment responses; 40psi pressure supply; 24ms solenoid period; 25% solenoid duty cycle; 5ms and 3ms time delay between two solenoids ........... 43 3.1 Valve lift profile with the solenoid action chart excluding system delays ................ 45 3.2 Valve lift profile with the solenoid action chart excluding system delays ................ 46 3.3 Level two model simulation and experiment responses ............................................. 50 3.4 Control parameter definition for case 1 and case 2 ........................................ 52 3.5 Model reference adaptive parameter identification scheme ............................... 54 3.6 Closed-loop valve lift and timing control scheme ........................................ 57 3.7 Control scheme with parameter identification based on model reference adaptation method ........................................................................................ 58 3.8 Cfl and C j2 identification simulation with fixed valve operation at 1200RP£I1 .................................................................................................... l 3.9 610 and (520 estimation simulation with fixed valve operation at 1200RPM ............. 62 3.10 Closed-loop valve lifi control at 1200RPM ............................................................. 63 3.11 Cfl and CfZ identification with 200 cycle valve bench data at 1200RPM ........... 65 3.12 610 and 520 estimation with 200 cycle valve bench data at 1200RPM ............... 66 3.13 The last valve lift profile at 1200RPM with the reference model output ............. 67 3.14 Cfl and Cj2 identification with 200 cycle valve bench data at 5000RPM ........... 68 3.15 610 and (520 estimation with 200 cycle valve bench data at 5000RPM ............... 69 xi 3.16 The last valve lifi profile at 5000RPM with the reference model output... . . . . . . ...70 3.17 Schematics of closed-loop valve lift control ............................................................. 74 3.18 Schematics of closed-loop valve opening timing control ........................................ 75 3.19 Schematics of closed-loop valve closing timing control ......................................... 76 4.1 Valve lift profile with the solenoid command chart .................................................. 79 4.2 Actuator piston model ................................................................................................. 81 4.3 ln-cylinder pressure model ........................................................................................ 83 4.4 In-cylinder pressure model validation by simulation ................................................. 86 4.5 In-cylinder pressure mode] integrated into exhaust valve model .............................. 87 4.6 Exhaust valve lift control strategy .............................................................................. 89 4.7 Feedforward exhaust valve lifi control strategy ......................................................... 91 4.8 Piecewise linearization of in-cylinder pressure .......................................................... 92 4.9 Closed-loop exhaust valve lifi control scheme ......................................................... 102 4.10 Simulation validation of feedforward solution without considering solenoid #2 delay ................................................................................................................................. 1 03 4.11 Simulation validation of displacement prediction. ................................................. 104 4.12 Simulation validation of velocity prediction ........................................................... 105 4.13 Model displacement with measurement noise injected .......................................... 106 4.14 Simulation validation of Kalman filter displacement estimation with measurement noise ....................................................................................................................... 107 4.15 Simulation validation of Kalman filter velocity estimation with measurement noise ........................................................................................................ 108 4.16 Simulation validation of closed-loop exhaust valve lifi tracking control system with four set points ............................................................................... 109 xii 4.17 Exhaust valve model identification with measured randomly varying valve back pressure .................................................................................................................. 1 11 4.18 Piecewise linearization of the measured exhaust valve back pressure force .........113 4.19 Calculation of the feedforward exhaust valve lift control inputs for three set points using the measured valve back pressure ................................................. 114 5.1 Top view of EPVA installed on the 5.4L 3V V8 engine head ........................... 1 17 5.2 Point range laser valve displacement sensors ............................................. 118 5.3 Pressure chamber underthe valve3118 5.4 Modular control system configuration ........................................................ 119 5.5 Control hardware 121 5.6 Solenoid driving circuit 122 5.7 Histogram of open-loop valve lift bench test data points for 9mm target lift at 1200rpm in 200 cycles 124 5.8 Histogram of open-loop valve lift bench test data points for 9mm target lift at SOOOrpm in 200 cycles 127 5.9 Open-loop parameter Cfl identification at 1200rpm ................................................ 130 5.10 Histogram of closed-loop valve lifi control test data points for 9mm reference lift at 1200rpm in 200 cycles ........................................................................................... 133 5.11 Steady state valve lift tracking responses from 9mm to 6mm lift at 1200rpm . 1 34 5.12 Controlled input and transient valve lifi tracking responses from 9mm to 6mm lift at 1200rpm ................................................................................................................ l 35 5.13 Steady state valve lift tracking responses from 6mm to 10mm lift at 1200rpm 136 5.14 Controlled input and transient valve lift tracking responses from 6mm to 10mm lift at 1200rpm ............................................................................................................... 137 5.15 Steady state valve lift tracking responses from 10mm to 7mm lift at 138 xiii 5.16 Controlled input and transient valve lift tracking responses from 10mm to 7mm lift at 1200rpm ............................................................................................................... 139 5.17 Steady state valve lift tracking responses from 7mm to 9mm lift at .................. 140 5.18 Controlled input and transient valve lift tracking responses from 7mm to 9mm lift at 1200rpm ................................................................................................................ 141 5.19 Valve lift tracking responses with multiple reference lift at SOOOrpm .............. 143 5.20 Histogram of closed-loop valve lift control test data points for 9mm reference lift at 5000rpm in 200 cycles .......................................................................................... 145 5.21 Experimental results of closed-loop exhaust valve lift tracking control system with three set points ...................................................................................................... 148 5.22 Enlarged experimental results of closed-loop exhaust valve lift tracking from set point of 8mm to 6mm ............................................................................................ 149 5.23 Enlarged experimental results of closed-loop exhaust valve lift tracking from set point of 6mm to 10mm ......................................................................................... 150 5.24 Enlarged experimental results of closed-loop exhaust valve lift tracking from set point of 10mm to 8mm ........................................................................................... 151 xiv CHAPTER 1 Introduction 1.1 Motivation and Literature Review In a camless valvetrain of an internal combustion (IC) engine, the motion of each valve is controlled by an independent actuator. There is no camshaft or other mechanisms coupling the valve motion to the crankshaft, contradicted to a conventional valvetrain. This makes it possible to control the valve events, i.e. timing, lift and duration, independent of crankshaft position. Various studies have shown that an engine equipped with variable valve actu- ation (WA) allows the reduction of IC engine pumping losses, deactivation of selected cylinder(s), flame speed regulation by manipulating in-cylinder turbulence, and control of the internal residual gas recirculation (RGR) and NOx emissions. These benefits contribute to a considerable potential engine performance improvement, fuel economy improvement and emission reduction . J.W.G.Turner et al. studied the strategies of camless valvetrain implementation [8]. Research has been conducted on different types of valve actuators, including electromagnetic, hydraulic and pneumatic actuators. Chihaya Sugimotoet et a1. [1], Mark A.Theobald et. a1. [11] and F.Pischinger et a1. [4] developed electromagnetic ac- tuators. H.P.Lenz et a1. [6] developed a hydraulic actuator. W.E.Richeson et al. presented a pneumatic actuator incorporated with a permanent magnet control latch in [17]. The advantages and disadvantages of a pneumatic actuator over a hydraulic actuator were ad- dressed by John P.VVatson and Russell J .Wakeman [14]. In their article, a pneumatic valve actuator with a physical motion stopper was presented and the simulations of the valve actuation system were shown. In [3], James E.Bobrow and Brian W.McDonell modeled a variable valve timing engine and discussed an engine control strategy. In order to provide an insight into the pneumatic actuator design and the control requirements, mathematical modeling was developed for a variety of actuation systems. In [7], J .M.Tressler et a1. an- alyzed and modeled the dynamics of a pneumatic system consisting of a doubleacting or single-acting cylinder and servovalve. A mathematical model of a pneumatic force actuator was presented by Edmond Richer and Yildirim Hurmuzlu in [16]. A significant amount of research has been conducted to demonstrate the advantage of variable valve actuation over the traditional cam-based valve-train of both gasoline and diesel engines. The investigation of intake valve timing control of a Spark Ignited (SI) engine was conducted in [5]. It was found that at low and partial load conditions, engine pumping loss was reduced between 20% and 80% due to throttless operation. Fuel consumption was improved up to 10% at idle. Through simulation and experiments, reference [13] shows that SI engine efficiency can be improved up to 29% due to Variable Valve Timing (VVT), compared to a classic (throttled) engine. The engine torque output is also improved by up to 8% at low speed with wide open throttle. Research carried out in [10] demonstrates how WT and VVL (Variable Valve Lift) affect the partial load fuel economy of a light- duty diesel engine. In this study, the indicated and brake-specific fuel consumptions were improved up to 6% and 19% respectively. The operation of an Otto-Atkinson cycle engine by late intake valve closing to have a larger expansion ratio than compression ratio was studied in [2]. A significant improvement of CO and NOx was obtained. Reference [18] also shows that the operational range of a Homogeneously Charged Compression Ignition (HCCI) engine can be expanded to operate at both high and low load through the adoption of WT and VVL. The advantages of WT and WL engines lead to the development of engine optimization over its operational range. For example, reference [12] presented the WT and WL optimization methodology for an I4 2.0L camless ZET EC engine at various operational conditions including cold starts, cylinder deactivation, full load, idle and transient operations. Electronically controlled pneumatic/ hydraulic valve actuators (EPVA) can be used to replace the traditional camshaft in an internal combustion engine. The EPVA is capable of varying valve lift height, valve timing and valve open duration as desired in a variable valve timing engine. In addition, the EPVA is designed to extract the maximum work from the air flow by incorporating a hydraulic latch mechanism to reduce the power consumption. A hydraulic damper mechanism is also added to produce a desirable slow and smooth seating velocity when the valve returns to the seat. This research is targeted to develop closed loop control strategies for both EMVA intake and exhaust valves to accurately regulate valve opening timing, lift and duration. For intake valves, an adaptive feedforward control scheme is developed to improve steady state and transient response performance; and for exhaust valves, model based predictive feedforward control strategy is employed to compensate the cycle-to—cycle varying in-cylinder pressure disturbance. Both control strategies were validated on the EPVA test bench using a Ford 3 valve 5.4 L V8 engine head. 1.2 Scope of Work and Content of Thesis The thesis is organized as follows. In chapter 2, mathematical models were developed to better understand the valve dynamics and to be used for control strategy development. A system dynamics analysis is provided in Section I followed by a mathematical model in Section II. This modeling approach uses the Newton’s law, mass conservation and ther- modynamic principles. The air compressibility and liquid compressibility in the hydraulic latch are modeled. The discontinuous nonlinearity of the compressible flow due to choking is carefully considered. Provision is made for the nonlinear motion of the mechanical com- ponents due to the physical constraints. Validation experiments were performed on a Ford 5.4 liter 4-valve V8 engine head with different air supply pressures and different solenoid pulse inputs. Experimental results are presented in Section III. The chapter ends with a few conclusions. Chapter 3 proposed an adaptive valve lift and timing control schemes for an electro- pneumatic valve actuator (EPVA) to improve both transient and steady state response performances. A control oriented electro—pneumatic valve model was developed in section I. An adaptive parameter identification scheme was developed based upon this model to construct a feedforward control in the next section. A PI (Proportional and Integral) closed- loop control strategy of valve lift and timing tracking was integrated with the feedforward control based upon the adaptive parameter identification. In Section III, the control algo- rithms were implemented in a prototype controller on an EPVA valve test bench using a 5.4 liter 3—valve V8 engine head. The adaptive parameter identification convergence was demonstrated during the EPVA bench tests and the closed-loop lift control algorithm was also evaluated by simulations. In Section IV, the detailed closed-loop intake valve lift, opening timing and closing timing control schemes were addressed. The conclusions were presented in Section V. Unlike the intake valve, the exhaust valve opens against an in-cylinder pressure that varies as a function of the engine operational conditions with cycle-to—cycle combustion variations. This pressure disturbance slows down the valve actuator response and as a result, it increases the variation of valve opening delay. In fact, this disturbance makes it difficult to maintain repeatable valve opening timing and lift. As a result, unrepeatable valve lift affects the closing timing control which is critical for RGR control. Therefore, addresses the exhaust valve lift control strategies in a way different from that of intake valve. In chpter 4, the level two dynamic model of the exhaust valve, along with the in- cylinder pressure model, is reviewed in Section I. The feedforward and closed-loop control strategies are discussed in Section II where a model-based predictive control technique was used to estimate the solenoid actuation timing for a desired valve lift. This estimation is used as a feedforward control, along with a PI closed loop control, to improve the exhaust valve lift repeatability. Then, the simulation validation results of the closed-loop exhaust valve lift control are shown in Section III. The real time exhaust valve lift control algorithm is depicted in Section IV, followed by the conclusions in section V. The valve model, intake and exhaust valve control strategies were developed from chap- ter 2 to 4. In chapter 5, the developed closed-loop intake and exhaust lift control systems are validated with experiments. Section I describes the EPVA experimental setup including both the mechanical system and the modular control system hardware configurations. Sec- tion II shows the real-time control results, along with data analysis for the lift and timing control of intake valves with concluding remarks. Finally, Section III presents the closed loop control test results for the exhaust valve lift control with concluding remarks. Images in this dissertation are presented in color. CHAPTER 2 Mathematical Modeling 2.1 Introduction In this chapter, a physics oriented nonlinear mathematical model of the electro—pneumatic valve actuator. It provides an insight to the mechanical system and help to develop control cetraria. 2.2 System Dynamics The EPVA consists of two solenoids, two spool valves, two port valves, an actuator piston, an actuator cylinder and a hydraulic latch/ damper system. An actuator piston pushes the back of the poppet valve stem, causing the valve to open. Solenoid-controlled spool valves are used to control the flow of the air that enters and exits the actuator cylinder. In order to reduce the energy consumption, EPVA uses a hydraulic latch which allows the actuator to extract the full expansion work out of the air that is drawn into the actuator cylinder. Meanwhile, the actuator is still capable of holding the valve in an open position to obtain full variation of valve open duration. A hydraulic damping mechanism is added to provide a slow seating velocity for the valve. According to the events taking place in the actuator cylinder, the system dynamics are divided into three stages: air charging, expansion and dwell, and air discharging stage. Figure 2.6 illustrates their equivalent stages on the valve lift profile. 2.2.1 Air Charging Stage p spool valve 1 spool valve 2 s“Pl-"'1! V2 + ‘ Q solenoid 1 . solenoid 2 outlet port valve inlet port valve inlet valve spring Figure 2.1. System dynamics at the air charging stage Figure 2.1 depicts the system dynamics when the actuator cylinder is at the air charging stage. The red color represents the high pressure (supply pressure) air, the blue color represents the low pressure (atmospheric pressure) air, the yellow color represents the oil in the hydraulic latch/damper. S 1 and 52 are two check valves that are corresponding to solenoid 1 and solenoid 2. When a solenoid is energized, its corresponding check valve is able to function as a one-way flow valve. When that solenoid is deactivated, then the check valve is held off its seat allowing two way flow. Green is an energized solenoid while blue is an de-energized solenoid. During the charging stage, solenoid 1 is energized pushing the spool valve 1 slightly to the right. In this spool valve position, the high pressure air is sent to two places, the left of the outlet port valve and the right of the inlet port valve. The low pressure air is sent to the left of the inlet port valve. Therefore, the high pressure air closes the outlet port valve and opens the inlet port valve. The supply air now charges the cylinder, the actuator piston starts moving down and opens the poppet valve. Although the right side of the outlet port valve is then subject to high pressure air, it remains closed due to the area difference between the two sides of the port valve. The check valve 5'1 is activated at the moment when solenoid 1 is energized. This only allows the oil to flow down the passage and prevents it from returning to the reservoir. The oil supply pressure is the same as the air supply pressure. 2.2.2 Expansion and Dwell Stage p _ spool valve 1 spool valve 2 sup ply V2. solenoid 1 solenoid 2 outlet port valve inlet port valve inlet Figure 2.2. System dynamics at the expansion and dwell stage In the expansion and dwell stage as shown in Figure 2.2, solenoid 2 is energized as well. The time delay between the activation of two solenoids is usually chosen from 2ms to 5ms depending on the desired valve lift height. The spool valve 2 is pushed slightly to the left so that the high pressure air can be sent to the left of the inlet port valve through the second spool valve. The check valve S2 is activated at the same time when solenoid 2 is energized to prevent the high pressure air from escaping to the atmosphere through the first spool valve. The inlet port valve is closed due to its area difference at two sides. Meanwhile, solenoid 1 remains energized, therefore, the outlet port valve remains closed. The air that was drawn into the actuator cylinder during the previous (air charging) stage is able to expand completely. The actuator piston and poppet valve both reach their maximum displacement. The high pressure oil (yellow color) trapped in the hydraulic latch (check valve S 1 is still on) balances the valve spring force and keeps the poppet valve open at its maximum lift height as long as it is needed. This is also called energr saving mode. It allows the system to extract the full expansion work from the air which has entered the cylinder without. losing the capability to vary the valve open duration. 2.2.3 Air Discharging Stage In the air discharging stage, the air leaves the actuator cylinder and the valve returns to its seat. As displayed in Figure 2.3, both solenoids are de-energized. Consequently, both check valves, 5 1 and S2, are deactivated. The air flow and the oil flow can travel in two directions. Since both solenoids are off, the springs inside the two spool valves can return the spools to their original positions. The high pressure air is then sent to both sides of the inlet port valve. The area difference between two sides of this port valve causes it to remain closed. Meanwhile, the low pressure air is on both sides of the outlet port valve. Because the oil in the hydraulic latch is now able to flow back up to its reservoir, there is no resistance for the valve spring to return the actuator piston. The actuator piston comes back and the volume of the air in the actuator cylinder is then reduced. This results in an increase of the air pressure in the actuator cylinder and an increase of the air pressure at the right side of the outlet port valve. Therefore, the outlet port valve is pushed open, the air in the actuator cylinder is able to discharge and its pressure decreases immediately. The poppet valve now returns to the seat. The hydraulic damper starts to function when Psu I spool valve 1 spool valve 2 pp y V1 v2 + a solenoid 1 solenoid 2 Patm 52 outlet port valve inlet port valve oil 81 outlet inlet imuatombton valve spring I w Figure 2.3. System dynamics at the air discharging stage the poppet valve moves close to its seat. Due to the decreasing flow area where the oil leaves the passage. the velocity of the valve is reduced greatly to provide a smooth return. 2.3 Mathematical Modeling The purpose of this section is to derive governing equations of the individual components of the pneumatic / hydraulic valve actuator, which consists of the actuator piston, the hydraulic latch/damper, the inlet and outlet port valves, two solenoids and two spool valves as displayed in Figure 2.1. These equations were used to simulate the behavior of the valve under different sets of operating conditions. 2.3. 1 Actuator Piston In this section, energy conservation, mass conservation and Newton’s second law were used to determine the following variables: the rate change of the gas pressure inside of the cylinder chamber Pp, the rate change of density of the gas [5,, and the acceleration of the actuator piston y'. A sudden reduction in pressure occurs at the inlet port when it opens. This causes the air flow to expand in an explosive fashion. The flow is choked and the pressure at the port stays constant. The difference between the cylinder pressure and the supply pressure decreases as the pressure in the cylinder chamber builds up over time. The air then becomes unchoked and flows through the inlet with decreasing pressure. The flow exiting the outlet switches between a choked and unchoked pattern as well for the same reason. This discontinuous nonlinearity of the flow has to be taken into consideration in the actuator piston model. As shown in Figure 2.4, considering the control volume above the actuator piston in the cylinder chamber including the inlet and outlet, the first law of thermodynamics can be written as: 2 2 . . tt- i. 6E Q—W+m,(h,-+—2‘—)—ni(.(he+1—°) = — (2.1) where, Q is the heat transfer rate into the control volume W is the work rate delivered by the control volume to the actuator piston m, is the mass flow rate entering the control volume - me is the mass flow rate exiting the control volume ii,- is the enthalpy of the gas entering the cylinder chamber he is the enthalpy of the gas exiting the cylinder chamber 9%- is the rate of change of the total energy of the control volume. Evaluation of W 11 The rate of the work done on the actuator piston by the control volume is: where, Ap is the area of the actuator piston, Pp is the pressure of the control volume (the pressure on the actuator piston) and t) is the velocity of the actuator piston movement. . ”ll-2 12 0 Evaluation of h, + j- and he + 4f The supply air entering the cylinder chamber from the inlet. can be viewed as a gas coming from a reservoir. The gas in the reservoir has zero velocity, therefore, its enthalpy is stagnation enthalpy of the inlet supply air hm. For the same reason, the air leaving the cylinder chamber from the outlet can be viewed as a gas leaving a reservoir, which is the control volume inside the chamber. Hence, the enthalpy of the air leaving the chamber can be represented by the stagnation enthalpy of the air in the actuator cylinder hp. .2 1.]. hi + 31 = hm = Cme (2-3) Treating air as an ideal gas, we have: P = pRT (2.5) . . . . P Replacmg Tp in Equation (2.4) With pp: 2 t.‘ C P h _C __ I) P . e. + 2 Rpp (2 6) where, - Tm is the temperature of the air at the inlet. which equals to the ambient temperature - Cp is the specific heat of the air at constant pressure — R is the gas constant. of the air 12 - pp is the density of the air in the cylinder chamber above the actuator piston - Pp is the pressure of the air in the cylinder chamber above the actuator piston - TI, is the temperature of the air in the cylinder chamber above the actuator piston 0 Evaluation of m, and 771.6 In order to draw the equations for the mass flow rate when the air flow enters the inlet or leaves the outlet, we need to consider two cases, choked and unchoked gas flow. The proof of the derivation of the mass flow equation is shown by J. M. Tressler et al. in [7]. We assume that the gas flow in the valve actuator is adiabatic (Q = 0) for now, and a term proportional to W will be subtracted from the total power that is delivered to the actuator piston to compensate the heat loss [16]. We also assume that the flow is isentropic everywhere except across normal shock waves. Considering the mass flow rate m, at the inlet, the flow patten depends on the cylinder pressure Pp and the supply pressure Rsupply as follows: , 1: mi = A(in RTRsupplyAin In If Pp > 0.53P9upp1y, the unchoked case: Ir. 1 l—k I k — 1 Psapply P 8111111121 If Pp S 0.53P9.,,pp1y, the choked case: ”Yin = 0.58 (2.9) where, k = 6% is the spec1fic heat ratio, CU is the specific heat of air at constant volume. Am is the area of the inlet. Since the port valves open and close very fast, the effective flow area Am can be approximated as: Am = wrf. w > 0 Am = 0, w = 0 13 (2.10) (2.11) where, 7'1 is the inner radius of the inlet port valve. We can derive the mass flow rate me equation similarly as follows: . k me = Tout R—TpPpAout (2-12) If Pout > 0.53Pp, the unchoked case: 2 Pout A Pout l—k ‘. . 1 “on = 2‘ T — 2 ' it k_fi,,> Kg) 1] (me If Pout S 0.53Pp, the choked case: Tout = 0.58 (2.14) where, Aout is the area of the outlet, it follows the same expression as Am except that it is dependent on 2. The Am“ expression can be given as below: A0“. = mi z > 0 (2.15) A0,, = 0, z = 0 (2.16) where, T1 is the outer radius of the outlet port valve. - 6E 0 Evaluation of W The rate of change of the total energy of the control volume is the summation of the rate of change of the internal energy, the kinetic energy and the potential energy. The kinetic and potential energy of the control volume are negligible. Hence, the change of the total energy is approximated as the rate of change of the internal energy: 6E 6U d T’)? _ .67 ._ a(vaTp) (2.17) m is the mass of air in the control volume and Cu is the specific heat of air at constant volume. The expression for in is: m=eay (me Expanding Equation (2.17), and using Equation (2.18) and Equation (2.5) results in: a—E_ _ ApCv 8t _ R (Pp!) + Ppy) (2.19) 14 The expression for Pp can be derived by substituting Equation (2.2), (2.3), (2.6), (2.7), (2.12) and (2.19) into Equation (2.1): - I PP = Z17?!"[CdinA-in(’u")Psupply7in kBRTi (220) k3P3 P ° _CdoutA0ut(z)70ut _£] - apkiy Pp y where, Cd,” and Cdout are the flow discharge coefficients at the inlet and outlet. (1,, is multiplied by the rate change of work W because it is assumed that part of the work is dissipated as heat loss from the system. ap is chosen to be between 0 to 1 depending on the actual heat loss during the process. This formulation is studied by Edmond Richer and Yildirim Hurmuzlu in [16]. Applying the law of mass conservation to the control volume above the actuator piston in the cylinder results in: mi ‘ me = Apfppll + Ppy) (2-21) Replacing m,- and me by Equation (2.7) and (2.12) to obtain the expression for p'p: . 1 ] k Pp = :21;[Cd'inAin(wh'inpsupply ET; (2°22) ‘CdoutAout(Z)A/outv kappl " p—zg Now we invoke Newton’s second law to obtain the 3] equation: My + 0ng + Kp(y + 6,.) = APPJD + Aw,pP0,-, (2.23) _(Ap + Ampipatm 1 M = Alpiston + Alva-Ive + 3 Mspring + Nicap where, 15 - jwpiston is the mass of the actuator piston - Almlvc is the mass of the intake valve - 1115]”,an is the mass of the valve spring. The effective spring mass equals one third of the total spring mass [15] - AIL-up is the mass of the cap on the top of the valve stem — Amp is the area of the cap on the top of the actuator piston stem - Ap = mg - Fng-l with rp as the radius of the actuator piston and rm) as the radius of the oil passage - C f is the damping coefficient approximating the energy dissipation due to the friction - KP is the stiffness of the valve spring 6;, is the preload of the valve spring Rearranging Equation (2.23): .. 1 . y = MIAPPP + Aoilpoz'l - (Al) + Aminputm — ny _ Kp(y + (spll (2°24) 2.3.2 Hydraulic Latch/ Damper Another mechanism that has a direct impact on the dynamics of the actuator piston is the hydraulic latch/damper. The compressibility of the fluid in the hydraulic latch is considered and the mechanism of adjusting the valve seating velocity is modeled in detail. Figure 2.5)illustrates this function. The oil sits on the top of the actuator piston stem with the supply pressure as the back pressure. Fluid enters or exits through area Amjlm/Am-laut. When the air that is drawn in at the air charging stage is fully expanded in the actuator cylinder, the actuator piston reaches to its maximum displacement. The check valve S 1 is activated by solenoid 1 to prevent the oil from returning. (Recall system dynamics at the air charging stage, and expansion and dwell stage.) The pressurized oil is trapped in 16 the passage and keeps the actuator piston at the maximum displacement until solenoid 1 is turned off. (Recall the air discharging stage). Hence, this hydraulic latch provides an adjustable valve open duration. Another function of this mechanism is to provide a low seating velocity for the valve. When the actuator piston approaches the original position, the cap on the top of the stem will partially block the exit area A. The actuator piston encounters a large resistant force due to the reduced flow area, which decreases the velocity tremendously. The smaller the area A, the lower the valve velocity. Figure 2.6shows a valve lift profile with the solenoid action chart. The solenoid itself has about 2ms to 3ms delay upon activation. These delays were not shown in this chart. As was explained earlier, one valve cycle consists of three stages: air charging, expansion and dwell, and air discharging stage. They will be called stage I, stage II and stage III in this section. Solenoid 1 is on at the beginning of stage I and off at the end of stage II. Solenoid 2 turns on before stage II. Solenoid 2 runs on the same frequency and the same duty cycle as solenoid 1 with a time delay. Both inlet and outlet are closed during the overlap of solenoid 1 and 2. The oil is modeled as an incompressible flow at stage I and III, while in stage II it is modeled as a compressible flow under high pressure with high incompressibility. The slight compressibility is what causes the volume change in the oil passage, hence the swing on the top of the valve lift profile. 0 Stage I Air Charging (Incompressible Flow Model) Psu ly _ Pail . go” = CdoilinAOilin\/ ppp 'l = Amp?! (225) 01 Therefore, the pressure of the oil at air charging stage is: Amp?) 2 Cd ) pail (2'26) Poilzpsuimly"( A .. 01-1,,” 011271 where, - 90231 is the volumetric flow rate of the fluid - Cdoilin is the discharge coefficient as the fluid enters the passage 17 - Again is the area where the fluid enters the passage (it is calculated later) - Psupply is the air supply pressure P0,) is the oil pressure and is at the same pressure as air supply pad is the density of the fluid Stage II Expansion and Dwell (Compressible Flow Model) The state equation PVC = K = constant is used here by choosing c very large to represent the high level of incompressibility. Poillockvc = 1"in (2.27) Substituting V = Amp-y and V,- = Awpy, into Equation (2.27) to obtain: Pitt/f Poillock = yc (2.28) Where, P051106), is the pressure of the oil at the dwell (lock) stage y,- is the maximum valve displacement V,- is the volume of the fluid at the maximum valve displacement y, P,- is the oil pressure P0,) at the peak valve lift height y,- Stage III Air Discharging (Incompressible Flow Model) Similarly, the equation of motion for stage III was obtained as follows: P ' — P I . 07. Rearrange Equation (2.29): Aca y 2 P -, = P 1 + 'P p -) (2.30 oz supp y ( Cdoz‘lautAo'ith) or ) where, 18 ‘Cd 01.th is the discharge coefficient as the fluid exits the passage - 140,10,“ is the area where the fluid exits the passage Amjin=Am10ut=A Evaluation of A: A = 2mg... + (Am-z — Amp). y s m (2.31) A = 274%)? + (Am-z — Amp). y < p1 (2.32) The variables rpass, A0,), Amp and 191 are shown in Figure 2.5. The seating velocity is largely reduced while the stem enters the area where y < 191. By adjusting m, we can alter its timing of entering the region where y < p1 and consequently the slope of the response. 2.3.3 Inlet Port Valve As illustrated in Figure 2.7) the inlet port valve is modeled as a mass-spring-damper system driven by the air flow from the spool valve with pressure Pcup R and the supply with pressure Psupply- Pcup R alternates between atmosphere and supply pressure which is regulated by the spool valve. Due to the difference between the areas on which PcupR and Psupply act, the port valve remains closed when P0,,p R equals Psupply and the supply air pushes it open when PmpR reaches atmosphere pressure. The supply air is treated as a stagnant flow with constant pressure. We obtain the equation of motion by Newton’s second law as below: mam?! + Comb + Kch = PsupplyAinlet — PcupRAcR (2-33) 0 S to S wmax, Amjct = arg - mg, AcR = 711% me R is the mass of the inlet port valve Co]? is the damping coefficient compensating for the friction loss of the valve KcR is the spring constant - w, ii), iii are the displacement, velocity and the acceleration of the inlet port valve 19 - trim” is the maximum distance which the inlet port valve is allowed to travel. The discontinuous nonlinearity in the port valve dynamics caused by this physical limita- tion was considered. — 7'2 is the outer radius of the inlet and outlet port valve (see Figure 2.4)). Rearranging Equation (2.33) to obtain expression for if": 1 w = fi(AinlctRsupply _ PcupRAcR — Cch _ Kch) (234) 'c 2.3.4 Outlet Port Valve The outlet port valve functions in a similar way as the inlet port valve, except that the air that pushes the port valve open has the actuator cylinder pressure. The pressure in the actuator cylinder is unsteady, thus, the flow dynamics were modeled. The modeling process is similar to the actuator piston. The control volume used here is shown in Figure 2.8. Applying conservation of energy as shown in Equation (2.1), we evaluate W, Q5? h,- + If; ,2 he + if m, and rmj as follows: W = Achmz (2.35) AcL = WT; where, Pout is the pressure on the outlet port valve in the control volume. 8E 8U d . E — '52- — Et(mCLrT0ut) — AcLCv R (Pout?) + Print?!) (2'36) where z is the displacement of the outlet port valve, Tout is the gas temperature in the control volume and Pout is the gas pressure in the control volume. The ideal gas law, Equation (2.5), was used to derive Equation (2.36). Treating the air flow from the actuator cylinder and the ambient air as stagnant flow we have: t 2 ,2 '2' CpPp . + pp], = hp = (7pr = (2.37) 20 ,2 f (: he '1' —2' = hatm Z CpTatm (2'38) , ] k. 7712'. = 'l'inL ff—T—IJPPAOM = Aout’l'inLV kpppp (2.39) where Amt is the inlet area of the control volume. As it is drawn in Equation (2.15) and Equation (2.16). Amit can be approximated as: Aout = 777%, z > 0 (2.40) A0,, = 0, z = 0 (2.41) If Pout > 0.53Pp, the unchoked case: 2 Pout A—gfl Pout 1_k 1 = ‘/_ 2k T — 2 If Pout S 0.53Pp, the choked case: i’tnL = 0.58 (2.43) . ] k me = "I'outL ij—tPOILtAL = AL’loutL V kpout Pout (2.44) - on where, - out is the temperature of the gas in the control volume - out is the is the pressure of the air in the — pout is the density of the air in the control volume and A L is the outlet area of the control volume and is also a function of geometry and the displacement of the outlet port valve. AL = 27rr12 (2.45) If Pam, > 0.53P0ut. the unchoked case: / 2 Putin Mil Patm 1 — k 1 [OlttL k _ 1( Pout ) [( Pout ) ] ( ) 21 If Patm < 0.53P0ut, the choked case: 'loutL ._-_—. 0-58 (2.47) Here, the gas was assumed ideal and the nonlinearity of the flow was considered in Equa- tions (2.42), (2.43), (2.46) and (2.47). One can obtain the equation of Péut in the following form by substituting Equation (2.35)-(2.47) into Equation (2.1) and letting Q = aLW as it was treated in the actuator piston model: . 1 kP Pout = T[CdiyzLAOILt(Z)Pp'l"inLka _B _ CdoutL (2'48) ‘ cLZ Pp Pmtté AL (3)7(th RkTatm V kpout Pout] — 0L k Here, a L is a number from 0 to 1 depending on heat loss, and Cdm L and Cdout L are the discharge coefficients. Applying mass conservation law to the control volume results in: mi - me = A(:L(pouti' + poutz) (2'49) Replacing m, with Equation (2.39) and replacing Tfte with Equation (2.44) in the equation above, p07,“ equation can be written as below: . I pout = mlcdiriLAout(3)7inL V kpppp (2'50) C pouté ‘Cdo'utLALwyfoutL V kpoutpoutl " z Finally, Newton’s Second Law yields the equation of motion of the outlet port valve: "chE + CcLé + KCL = Aoutlctpout _ ACLPcupL (2-51) 2 2 0 S Z S 37710119 Amulet = 72TlsAcL : 7W2 - mC L is the mass of the outlet port valve 22 CcL is the damping coefficient compensating for the friction loss of the valve KC L is the spring constant - z, 2, 2' are the displacement, velocity and the acceleration of the outlet port valve zmax is the maximum distance which the outlet port valve is allowed to travel. The discontinuous nonlinearity in the port valve dynamics was considered in the simula- tion. Rearranging Equation (2.51) to obtain an expression for '2' results in: .. 1 . Z = m—(Aoutlctpout _ PcupLAcL _ CCLz - KCLZ) (252) C All the discharge coefficients that are involved in the flow equations were determined nu- merically and experimentally. 2.3.5 Spool Valve The armature of the solenoid pushes the stem of the spool valve with the magnetic force F 3 when the solenoid is energized and a pre-compressed spring returns the spool valve when the solenoid is de-energized. The spool valve is pressure balanced at two ends as shown in Figure 2.9. The equation of motion of the spool valve is: Where mspool is the mass of the spool valve, C3 is the damping coefficient modeling the frictional loss, K 3 and 63 are the stiffness and preload of the spring. 2.3.6 Solenoid A solenoid can be modeled as an RLC circuit as shown in Figure 2.10. The Kirchoff law writes: . di 23 Where, Vin is the pulse input voltage, 2' is the current, R and L are the resistance and the inductance of the solenoid. The relationship between the current i in the coils and the magnetic force F,- on the armature is assumed to take the following form: (712 1+g a Fs=L+ (2.55) Here, a and b are chosen to curve fit the empirical data provided by the manufacture. 2.4 Simulations and Experiments 2.4. 1 Experimental Setup Figure 2.11 displays the devices that were used in the experiments. A Ford 5.4 liter 4-va1ve V8 engine head was used for the valve test. The camshaft was removed on the intake valve side and an EPVA was installed above one of the intake valves. A Micro—Epsilon optoNCDT 1605 point range laser sensor was used to measure the displacement of the test intake valve. The laser sensor was mounted on an angle such that the laser beam from the emitter of the laser sensor would be perpendicular to the surface of the end of the valve stem. A dSPACE D81104 PCI board was used for control and data acquisition. A switching circuit made of IGBT’s (insulated gate bipolar transistor) amplified the signal from the computer and served as a driving circuit for the solenoids. Two STP2416—015 small push-pull solenoids were used to drive two spool valves in the EPVA. A DC power supply from Extech Instruments model 382203 was used to provide the electrical power for both the sensor and the circuit. The experiments were conducted under the combinations of various control parameters: - 30psi and 40psi supply pressure - 100ms, 40ms and 24ms solenoid durations that were corresponding to 1200rpm, 30007"an and 5000rpm engine speeds - 30% and 25% solenoid duty cycles 24 Table 2.1. The Matrix at iit arameters e com inations o ameter sets 11 V enoi ms en01 e v ween two . 1 ms Table 2.2. The t Matrix at 92' n ro arame e co inations o ter sets it v , ure enoi ms l I ICC y ween Two Solenoids ms - 5ms and 3ms time delays between the first solenoid and the second solenoid As given in Table 2.1 and 2.2. the experiment matrix listed 18 combinations of parameter sets under which the experiments were conducted, and the responses were compared with the simulation responses in the next section. The EPVA is aimed to tailor the engine intake flow without throttling. Therefore, in the experiments and simulations, the engine intake manifold pressure is considered to be close to atmospheric pressure. Since it is the intake valve that is being studied in here, no pressure loads are included on the valve head. In future studies where the exhaust valve will be studied, the valve will have to open against a high engine cylinder pressure. This model is capable of this type of simulation, but it is not included here since no experimental data is available for validation at this time. 2.4.2 Simulation The equations of motion derived previously were written in state space form and pro- grammed in S imufinkTM . The simulations were performed under the same parameter sets as were the experiments. The eighteen experiment and simulation responses are presented in Figure 2.12 through Figure 2.20. The dotted lines represent experimental responses and the solid lines represent the simulation responses. Figure 2.12 shows the responses under 30psi supply pressure, 100ms solenoid period with 30% duty cycle and 5ms vs. 3ms delay between two solenoids. The 100ms solenoid period corresponding to the engine speed at 25 1200rpm. The response with 5ms delay had about 6ms rising time and the response with 3ms delay had about 5ms rising time. The maximum valve lift height was 6mm for the response with 5ms delay and 3.8mm for the response with 3ms delay. The swing motion on the top of the profile shows that the valve is in the dwell stage when the hydraulic latch is utilized to hold the valve open. The slight compressibility of the oil in the hydraulic latch causes the oscillation of the valve response which damps out eventually. The hydraulic damper is initiated at 377723, where the slope of the response is largely decreased and the response approaches to the original position gradually afterwards. The responses in Fig- ure 2.13 were obtained under the same operating conditions as those in Figure 2.12 except that the solenoid period was reduced to 40ms, corresponding to 3000rpm. The rising time of the response with 5ms and response with 3ms were 67713 and 5ms. As the solenoid period is reduced, the dwell stage is shorter. The maximum valve lift height is 6mm for the response with 5ms delay and 4mm for the response with 3ms delay. The solenoid period then was reduced to 24ms, corresponding to 5000rpm. The responses are shown in Figure 2.14. In this case, the maximum valve lift is 5mm and the rising time is 6ms for the response with 5ms delay. The maximum valve lift is 4mm and the rising time is 5ms for the response with 3ms delay. The maximum valve lift height in the 5ms delay case is decreased from 6mm to 5mm. This happens because the solenoid is de—energized before the actuator piston can fully expand to its maximum displacement; the valve has to return without reaching its maximum lift. Moreover, the valve never enters the dwell stage in this pair of responses. The solenoid period is so short that the valve entered the air discharging stage immediately after the air charging stage. Hence, the swing motion disappears on the top of the profile. The experiment and simulation responses at 40psz' pressure supply with 30% and 25% solenoid duty cycles are presented in Figure 2.15 through Figure 2.20. The response rising time of the valve varies from 47713 to 6ms. The maximum valve lift is around 8mm for the response with 5ms delay and 6mm for the response with 3ms delay in this case. As was expected, the valve lift height could be controlled by regulating the supply pressure or varying the delay between two solenoids, and the valve open duration could be 26 controlled by controlling the activation duration of the solenoid. The mathematical model was able to capture the dynan‘iics of the EPVA closely. 2.5 Conclusions This article presented a dynamic model for an electrically controlled pneumatic/ hydraulic valve actuator. This model will be incorporated to develop criteria for both design and control of the valvetrain in a camless internal combustion engine. Two solenoids and two spool valves, a single acting cylinder, an inlet port valve, an outlet port valve, a hydraulic latch/damper and an intake valve with its valve spring were included in this model. The mathematical model employed Newton’s law, mass conservation and principle of thermodynamics. The nonlinearity of the flow, incompressibility and compressibility of the hydraulic fluid and the nonlinearity of the motion due to the physical constraint was carefully considered in the modeling process. The control parameters were studied. The model was implemented in Simulink / M atlabTM under different combinations of operation conditions. Validation experiments were performed on a Ford 5.4 liter 4-valve V8 engine head with various air supply pressures, solenoid periods, solenoid duty-cycles and time delay between two solenoids. The numerical simulation results were compared with the experimental data and showed excellent agreement. 27 outlet port valve inlet port valve lie—'51 Lizfl' Acap Psupply 2' . 0“ h' T v he Ve me In in In Tout I Ain reservior outlet port _l,—' f' F l inlet port I‘ Aou't _____ '— — hi vimi l y L fr _Pr>_ 1:9 _Tp_ E-V-J piston margin [All] of AL? Q44 Mvalve Figure 2.4. Actuator piston model 28 P1 Psupply Aoilinleilout Acap Figure 2.5. Hydraulic latch/ damper model expansion and dwell l| (Poilock) , air charging / air discharging | (Foil) ||| (Pail) A P—i — a I: O E e 2 5 - N E 3 E i; 1 hydraulic damper active zone time voltage 24V‘ 1- N 1- N E 12 E i E o o o o C C C C O O O G '6 l '5 at a O O 0 0 'It rt I A utlt rt l “m m e po va ve open 0 e po va ve open outlet port valve closed both inlet and outlet inlet port valve closed port valve closed Figure 2.6. Valve lift profile with the solenoid action chart 29 inlet port valve Psupply [.— Figure 2.7. Inlet port valve model Ii’atm Tatm Pphprpp outlet port valve Figure 2.8. Outlet port valve model 30 Psupply spool valve I] .r.’ 2b° i " 2323 v ”Psupply 1 l’a’tm Patm Psupply Figure 2.9. Spool valve model Figure 2.10. Solenoid model 31 Power supply Intake EPVA Solenoid ‘ Driving circuit . . mi"; Engine head Input/Out ut Host computer a ll~ f L. i Laser sensor dSPACE control board ' a?“ Figure 2.11. Experimental setup 32 30 psi air supply; 100ms period; 5ms delay; 30% pulsewidth A 0.01 I E 5 5 — - Experiment :7 0.008 r ------ —Simulation : . . 4 . g 0.006 ,---- --------- ~5- --------- -------- '1 8 0.004 r ------- l -------- «j ---------- § ---------- ;~ -------- - o 5 : : : : .3 a 0.002 gum"-.. ......... ;. ........ .. > a i i ' : i . _i 1 0 0.02 0.04 0.06 0.08 0.1 30 psi air supply; 100ms period; 3ms delay; 30% pulsewidth A 0.01 1 T x r E 5 : : : :7 0.008 ' ' 5 E 0.006 e o 2 71 0.004 7': ,2 0.002 > D 0 . time (see) Figure 2.12. Simulation and experiment responses; 30psi pressure supply; 100ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids 33 30 psi air supply; 40ms period; 5ms delay; 30% pulsewidth 0.01 ; 4 ‘g : —- - Experiment 3: 0.008 rr — Simulation 1: : : r g 0.006 ..---------.. -- ----------- a 8 0.00M ----------- 5 ----------- «E ------------ +j ----------- a g 2 : : : 7: .2 0-002 ----------- j > a A i j i 0 0.01 0.02 0.03 0.04 30 psi air supply; 40ms period; 3ms delay; 30% pulsewidth A 0.01 : 7 T e s s s 2.." 0.008 t* ----------- 4 5 E E i .5, 0.006 t ------------ 5“ ----------- *5 ------------ ‘5 ----------- _ g 0.004 r ----------- I ---------- ~§ ------------ «f ----------- 4 0 a : : : 7: ,2 0.002 .-------. "f'm *- """"""" r > o A - 1 J ._ 0 0.01 0.02 0.03 0.04 time (sec) Figure 2.13. Simulation and experiment responses; 30psi pressure supply; 40ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids 34 30 psi air supply; 24ms period; 5ms delay; 30% pulsewldth A 0.01 , . . E 3 5 — - Experiment : 0.008 r~ ----- — Simulation '3 : : 7 T “E' 0.006 ---------- 1 ---------- § ---------- g ------- , 8 0.004r ---------- g --------- . -------- f. ---------- g ........ o 3 : : : : 77. g 0.002 -.- ....... . > E . . i . . 0 0.005 0.01 0.015 0.02 0.025 30 psi air supply; 24ms period; 3ms delay; 30% pulsewidth g 0-01 j i z E :7 0.008 L«- -------- 5 E E E E E 0.006L --------- -; ---------- 4: ---------- ........ 0 l i l i 3 0.004» ---------- s --------- , -------- g ---------- g -------- g E E E E E a ,2 0.002 ~------~:---- ------- w > a . . . l l 0 0.005 0.01 0.015 0.02 0.025 time (sec) Figure 2.14. Simulation and experiment responses; 30psi pressure supply 24ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids 35 30 psi air supply; 100ms period; 5ms delay; 30% pulsewidth 0.01 . . é ; 5 —-Experiment ‘5 0.008 r---- . --~: --------- . ——-Slmulation 0 l i . T g 0.006 -~ ---------- ---------- .52 0.004. -------- i -------- «: ---------- a ---------- 1+ -------- - z 3 a 2 a a £5 °-°°2 :""""T """""" :' """" " l ' l i 0 0.02 0.04 0.06 0.08 0.1 30 psi air supply; 100ms period; 3ms delay; 30% pulsewidth E 0.01 3 y T T '5' 0.008r* ---------- ---------- ---------- g 0.00m -------- 4 --------- .; ---------- g ---------- g ........ .. a ' j __________ 5 __________ i __________ 3} °‘°°‘ : ’2 s :* gs 0.002 ......... -§- ......... ........ .. ' ' ' L l_ 0.04 0.06 0.08 0.1 time (sec) Figure 2.15. Simulation and experiment responses; 40pm? pressure supply; 100ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids 36 30 psi air supply; 40ms period; 5ms delay; 30% pulsewidth 0.01 . g g --- -- Experiment *5 0.008» ----------- an” ' —— Simulation o . l T g 0.006 r------_--- -§-------— ----------- a . .8 0.004r ---------- ----------- «j ------------ i ----------- ~ 2 3 __________ E .......... E ............ E ________ >0 a 0.002 f T *5 l '- "1 L L m 0 0.01 0.02 0.03 0.04 30 psi air supply; 40ms period; 3ms delay; 30% pulsewidth E °-°‘ T E T g 0.003 ‘ ' ' § 0.006 N 3 § 0.004 g a 0.002 0.02 time (see) Figure 2.16. Simulation and experiment responses; 40psz' pressure supply; 40ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids 37 30 psi air supply; 24ms period; 5ms delay; 30% pulsewidth 0.01 y . E . 3 — - Experiment *5 0.008 r -- -. —Simulatlon 0 l . 1 T g 0.006 r ----- \ ....... 1 «,2 0.004 r----------§ --------- i ------- \ ------- 4 z 8‘ a a = : g5 0.002 f --------- . ----------------- -1 J J i 0 0.005 0.01 0.015 0.02 0.025 30 psi air supply; 24ms period; 3ms delay; 30% pulsewidth E °-°1 T E E T g 0.008 ------- - 3 0.006 """"" "E """" 72:6: ------- 5‘ --------- a: ------- —. 3% 0.004 ---------- .; ----- 4.4m : 2 E3 0.002 L --------- -------- --------- ------- 4 . l . 0 0.005 0.01 0.015 0.02 0.025 time (sec) Figure 2.17. Simulation and experiment responses; 40psi pressure supply; 24ms solenoid period; 30% solenoid duty cycle; 5ms and 3ms time delay between two solenoids 38 30 psi air supply; 100ms period; 5ms delay; 25% pulsewidth é 0'01 — -Experiment ‘5 0.008 .---- . ----~: ---------- —'Simulatlon o : : . T g 0.006 P--- -----;.-... -'--~ -------- -1 . 2 0.004 ----- i -------- s ---------- g ---------- i -------- ~ > i l l i E 3 0-002 -- -------- ~ 1 ' ___l 4'_A 0 0.02 0.04 0.06 0.08 0.1 30 psi air supply; 100ms period; 3ms delay; 25% pulsewidth E °-°1 i E 7 r g 0.008 0 --------- -------- . § 0.006 --------- é --------- é ---------- é- --------- -------- 4 a ' ________ ' __________ E __________ i ________ A 3 *3 ”“4 . *5 a E‘ g a 0.002L -------- --------- ~;- --------- -------- - ' _' __ l __ A..- 0.04 0.06 0.08 0.1 time (sec) Figure 2.18. Simulation and experiment responses; 40psz' pressure supply; 100ms solenoid period; 25% solenoid duty cycle; 5ms and 3ms time delay between two solenoids 39 30 psi air supply; 40ms period; 5ms delay; 25% pulsewidth é 0'01 5_ § — - Experiment ‘5 0.008 ' I -— Simulation ° ' E i g 0.006 ------ g- ----------- -§ ------------ 4 a 3 0.004 E """ é- """""" é """"""" z 9- : : : g g 0.002 ------------ ----------- —- ----------- « i ; i 0 0.01 0.02 0.03 0.04 30 psi air supply; 40ms period; 3ms delay; 25% pulsewidth E ”1 I i i ‘g 0.000 ' ' ' § 0.006 a 3 -% 0.004 g a 0.002 0.02 time (see) Figure 2.19. Simulation and experiment responses; 40psz' pressure supply; 40ms solenoid period; 25% solenoid duty cycle; 5ms and 3ms time delay between two solenoids 40 30 psi air supply; 24ms period; 5ms delay; 25% pulsewidth é 0'01 i — -Experiment ‘5 0.008 r~ --------- ——-Simulation ° E /,I?‘\ i 7 g 0.006? --------- a: -------- ,4;---\ ----- ~ --------- . ....... 4 mg 0.004r ---------- § --------- i ---\ ------------- -: ------- a > : : 33 0.002r---------~:-- -------------------------- « > a ' i i t; 0 0.005 0.01 0.015 0.02 0.025 30 psi air supply; 24ms period; 3ms delay; 25% pulsewidth E 0.01 , I . 1 E 0.008 L ------- a 0.006% --------- é -------- ,:: é ---------- ~ --------- -§ ....... - é 5"/s\\ = “a 0.004» --------- ~, -------- ,--\ ------ . --------- .; ------- ~ 2 a, : : : g5 0.002~--------~;-; -------------------------- a - ' i L 3 0 0.005 0.01 0.015 0.02 0.025 time (sec) Figure 2.20. Simulation and experiment responses; 40psi pressure supply; 24ms solenoid period; 25% solenoid duty cycle; 5ms and 3ms time delay between two solenoids 41 CHAPTER 3 Intake Valve Control System Development 3.1 Introduction The physics based nonlinear mathematical model developed in the previous chapter is called the level one model. In this chapter, a control oriented model, the level two model, was created. The adaptive intake valve control scheme was established. The convergence of the derived adaptive parameter identification algorithm was verified using the valve test bench data. The intake valve closed-loop control strategies was developed and validated in simulation. 3.2 Level Two Model The level one model is a sophisticated nonlinear model which requires heavy computational throughput and is almost impossible to be implemented in real time. A control oriented model, called level two model, is needed in this case. 42 3.2.1 Review of System Dynamics EPVA consists of an actuator piston, a hydraulic latch (damper), inlet and outlet port valves, two solenoids and two spool valves. The actuator piston is driven by compressed air. It sits on the back of the valve stem. hence. its motion is equivalent to the valve motion. Figure 3.1 shows the schematic diagram of an EPVA. A detailed description of EPVA dynamics and level one model can be found in chapter 2. The level two modeling work concentrates on the piston (end actuator) dynamics and omits the nonlinear flow dynamics. As illustrated in Figure 3.2, the valve operation process can be divided into three stages. They are opening stage I. dwell stage II and closing stage III. p spool valve 1 spool valve 2 slllpply solenoid 1 H II solenoid + l H _ . v2 V1input input outlet port valve inlet port valve y f- - Mpiston ”glaring | 001m" - Mvalve .L47‘ Figure 3.1. Valve lift profile with the solenoid action chart excluding system delays 43 I II III open dwell lclose time 5 II" 1‘ | ill-1 air pressure forcei 24 volts ------------------ solenoid 1 solenoid 2 52 time 51 —. 1- begin air charging 2- end air charging 3- hydraulic latch deactivation begin air discharging 4- start to return against compressed residual air 5- hydraulic damper activation Figure 3.2. Valve lift profile with the solenoid action chart excluding system delays 44 3.2.2 Level Two System Modeling Opening stage In this stage the valve actuator is modeled as a second order mass-spring-damper system with zero initial conditions, see Equation (4.1). Mfl+Cf19+Kp(i/+6p) = W) -F(t-61) (3.1) F(t) — 0’ ift < 0 APP? + ACGPPOil _ (AP + Acaplpatm if t Z 0 where Pp = P0,, z Psupply, and - M = Mpiston + Mvalve + 313M spring + Mcap, where Mpiston is the mass of the actuator piston, Mvalve is the mass of the intake valve and M spring is the mass of the valve spring. The effective spring mass equals one third of the total spring mass [15], and Alcap is the mass of the cap on the top of the valve stem; - AP = 7TT'2 — 7r?“2 p oil with 1“,, as the radius of the actuator piston and r0.” as the radius of the oil passage; 'Cf 1 is the damping ratio approximating energy dissipation due to flow loss and fric- tional loss; - Kp is the stiffness of the valve spring; - 6,, is the preload of the valve spring; - Pp is the in-cylinder air pressure, P0.“ is the oil pressure and is at the same pressure as air supply, and Psupply is the air supply pressure; - Amp is the area of the cap on the top of the actuator piston stem; - 61 is the lag between the activation of solenoid 1 and 2 without system delays as illustrated in Figure 3.2, and 62 is the time needed for valve to return to the seat. 45 Dwell stage The equation of motion at stage II is described as follows: Mi} + deeuy + KN! + 5p) = ApPp + ACGPPm'llock (3-2) ‘(Ap + Acaplpatm where Pp z Patm since the supply pressure has been removed and the piston is fully extended at this stage, M is the total mass of the actuator system as described in Equa- tion (4.1), deell is the damping ratio approximating energy dissipation due to frictional loss at dwell (lock) stage, and P011106}, is the oil pressure applied to piston stem in dwell stage. The state equation PVC = K = constant is used to obtain the expression for Poillock where a large 0 value was chosen to represent the low compressibility. Poillockvc = Pivic (3'3) Substituting V = Acapy and V,- = Acupy; into Equation (3.3) to obtain: Pill? Poillock = y6 (34} where y,- is the maximum valve displacement, V,- is the volume of the fluid at the maximum valve displacement yi, and P,- is the oil pressure Pm'l at the peak valve lift height yi. Closing stage Dynamic motion in the closing stage was divided into two sub—stages (sub-stages III-1 and III-2) as illustrated in Figure 3.2. Substage III-1 can again be separated into two segments. The first segment is from point 3, where the piston starts returning, to point 4; and the second segment is from point 4 to point 5 where the hydraulic damper becomes effective. In the first segment, piston motion is a free return, however, in the second segment, the piston returns against certain pressure due to in-cylinder compressed residual air. For simplicity, both segments were modeled as free returns. In substage III-2, the piston returns against largely increased hydraulic damping force that acts on the piston stem. The governing 46 equations at this stage are described in Equations (3.5) and (3.6). Equation (3.5) describes the response from point 3 to 5 (see Figure 3.2). Il-J;ij+Cf2y+pr+Kp6p = 0 (3.5) where y(0) = ymax, and 9(0) = O. The response beyond point 5 in hydraulic damping region follows the response of Equation (3.6). _(Ap + Acaplpatm where P0,; is a constant in substage III-1. But it is a function of flow out area in the hydraulic damper in substage 111-2. The detail derivation of P0,, can be found in chapter 2. 3.2.3 Level Two Model Validation The simulation and experimental responses of the level two model are compared in F ig- ure 3.3. The thin valve curve is the experimental response; and the thick one is the simulated response using level two model. Damping ratio at opening stage, C f1, and damping ratio at closing stage, C f2 are identified manually by trial and error in this simulation. In the real time implementation, these damping coefficients will be adaptively identified online since they vary significantly with respect to temperature, fluid viscosity and engine operational conditions. The two curves close to the x axis are the measured solenoid currents, where the solid line is the dwell current of solenoid 1 and the dash line is that of solenoid 2. There are delays between the activation of the solenoids and the actual mechanical motions. The total delay associated with solenoids 1 and 2 are defined as Atl and Atg respectively. As shown in Figure 3.3, total delay of each solenoid rises in two steps. Taking solenoid 1 cur- rent as an example, the first rise is from the starting point to the first peak which represents the electrical delay; and the second rise is from the first peak to the second peak which 47 represents the magnetic delay. Algorithms were developed to detect Atl and Atz at each cycle. Atl is used to follow reference opening timing by compensating the valve opening delay. Both Atl and A122 are used to modify the pulse width of air pressure force input 61 associated with the valve lift control. This will be discussed in the next section. 12 31m E E3. 8. 515 2'3 53 5" 5,2 3?, 4* a: '63 2- °), " 0202” 0.04 0.06 0.03 0.1 time (sec) Figure 3.3. Level two model simulation and experiment responses 3.3 Control Strategy The control strategy of valve timing, duration, and lift is addressed in this section. An adaptive parameter identification algorithm using model reference technique and MIT rule [9] played an important role in the control process. The identified parameters are then used to modify parameters in the closed-loop controller. Some approximations are introduced to obtain analytical solutions of control input in terms of the estimated parameters. To further reduce the computational efforts, only stages I and III of level two model were used in the controller. (see Figure 3.2). Parameters involved in the control process were investigated and defined for three possible cases. The closed-loop control scheme is proposed and the 48 concept is validated in simulation for closed-loop valve lift control. The closed-loop valve open and close timing control portion is similar to the valve lift control, and the results are not repeated in this section. 3.3. 1 Parameter Definition Figure 3.4 defines the parameters involved in control strategy. At low engine speed, the valve lift profile has all three stages as shown in the top diagram, where the holding period exists. This kind of response is categorized in case 1 (with holding). As engine speed increases, the holding period reduces. At certain engine speed, the holding period disap— pears, and the valve lift profile consists of only the opening and closing stages as shown in the bottom diagram. That is named as case 2 (without holding). In this case, solenoid 1 was deactivated shortly after its activation. It discharges the cylinder and allows valve to return before the hydraulic latch is engaged. In these two cases, both solenoids 1 and 2 are needed to control the valve event. There is another special case in which only solenoid 1 was used. The cylinder was simply charged with supply air when solenoid 1 is energized and discharged when solenoid 1 is de—energized. This occurs when the engine speed is so high that the activation duration of solenoid 1 becomes very small. The valve lift control is implemented by regulating air supply pressure in this case. Note that in both cases 1 and 2, the air supply pressure remains unchanged throughout the process. This special case is not the subject of discussion in this paper. As displayed in the left diagram of Figure 3.4, control pulses of solenoids 1 and 2 are generated based upon De f A and De f B pulses that are synchronized with engine crank angle. Def B appeared to be nonzero during the time Def A was sent, when the system needs to utilize both solenoids 1 and 2. Def A and De f B pulses carry the control information and they will be converted to solenoid command pulses. The convention of this transformation is defined as follows. The first and second rising edges of De f A correspond to the activation of solenoids 1 and 2. The first and second falling edges of De f A correspond to the deactivation of solenoids 1 and 2. The first pulse width of De f A is denoted as 51 and the second pulse width of De f A is denoted as (52. 51 49 Case #1 (With holding) Case #2 (Without holding) solenoid 2 ~ 4' 9 2 tim:e " dwell Ill closing stage ‘ y 62 |<— time DefB I l Def 3 5 voltage T 1] I 2 l6 24V solenoid 2 solenoid 1 = M1 = time: _ +IA‘2I+- . I opening stage III closing stage force l |<- ti —>| 82 [<— Figure 3.4. Control parameter definition for case 1 and case 2 50 is the time duration between the activation of two solenoids. The second falling edge of Def A, which is also the falling edge of solenoid 2 pulse, is defined to be the desired valve closing time. 62 represents the time needed for the valve to return after the deactivation of solenoid l (at valve return point). Activation of solenoids 1 and 2 begins their impact on the system after time delays A231 and Atg respectively. The air pressure in the piston cylinder rises and forms a pulse force input to the system with a pulse width 61. Therefore, 51 associates with 61 through the expression 51 = 61 +(At1 - Atg), given the fact that Atl is always greater than Atg. The parameter convention described in the right diagram of Figure 3.4 for case 2 is similar to case 1. For both cases, desired valve opening and closing timing and desired valve lift are known variables. 3.3.2 Adaptive Parameter Identification The architecture of adaptive parameter identification is illustrated in Figure 3.5, where Gm(S) is the model and 019(5) is the plant. The goal of this estimator is to identify the damping ratios C f1 and C f2, where C fl is for the opening stage and C f2 is for the closing stage. The error 6 between model and plant outputs reduces as the estimated parameters converge. The excitation force u is a pulse input with PE of order infinity that meets the persistent excitation condition in the adaptive identification. The identification controller based on MIT rule utilizes the error between the model and plant outputs and generates the estimated C f1 or C f2, where C f1 and C f2 update at every step during the identification period. MIT rule MIT rule states as follows. 51 -------------------------------------------------------------------------------------------------------------- 5 ___. Gmlsl model I MIT rule éfm uE - Gp($) _i_©e_lq=4yevcfe _ plant model reference adaptive parameter estimator ”l" . 0 I oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo J Figure 3.5. Model reference adaptive parameter identification scheme where y, valve displacement, is the plant output and ym is the model output of valve displacement, e is the error between the model and plant outputs, 0 is the estimated parameter, and 'y > 0 is the adaptive gain. In this case, 6 _ C f1 , for opening stage — C f2, for closing stage Adaptive law at opening stage In this section and the following section, the adaptive law at opening and closing stage is developed based on the MIT rule. The governing equation of the system at this stage is expressed in Equation (3.9). where y(0) = —6p, 9(0) = 0, and u(t) = F(t) — F(t — 61) by Equation (4.1). To change the coordinate, let Equation (3.9) can be rewritten in z coordinate as below: M2+Cf12+sz=u(t) (3.11) where 2(0) = 2(0) = 0. Laplace transform of Equation (3.11) results in Equation (3.12): M52 + Cflszw) + 192(5) = 0(3) (3.12) 52 The transfer function takes the following form: _ 2(5) _ 1 — U(S) " M52 + Cf15 + KP The error between the model output and the plant output in Laplace domain E (S) can be 0(5) (3.13) expressed in the equation below: 1 _ MS2 + Cf15 + Kp _ 1 MS2 + CfmlS + KP E(S) = Z(S) - Zm(S) [1(5) (314) U(S) where Z and Zm are the plant and model outputs, and C f1 and Cfm1 are the plant and model damping ratios. Let P(S) = 6135 . We obtain P(S) by taking partial derivative m1 of E(S) with respect to Cfml: U(S) S P S = .1 ( ) M52 + Cfmls + Kp M52 + Cfmls + KP (3 5) . U S . . Since M32+Cf(m)15+Kp = Zm(S) by Equation (3.14), Equation (3.15) can be rearranged into Equation (3.16) : S 1 K M S + C fml + f Taking the inverse Laplace transform of Equation (3.16) to obtain the adaptation law of P(S) = Zm(S) (3.16) = Zm(S) 15(t) results in Equation (3.17). pm = fiwt) — 0mm) — Kp /p(t)dt) (3.17) The adaptation law of C f1 at opening stage is summarized below: Cfml = —'71p(t)e pa) = mane) — Cfmlpu) - Kp f p(t)dt) 5’ = Z “ 2m = y — Elm with '71 > 0 chosen to be an adaptive gain. The adaptation takes place between point 1 and the first peak on the valve response as indicated in Figure 3.2. 53 Adaptive law at closing stage The adaptive law of C f2 at the closing stage can be derived in a similar way to the opening stage, and the result is presented below. Cme = “72(1(t)e (10') = 31%](zmit) — CmeQU) — Kpfq(t)dt — f 2(0)dt) 8:2'31n=y_ym with 72 > 0 being an adaptive gain and C fm2 being the model damping ratio. The adap- tation occurs between points 3 and 4 as indicated in Figure 3.2, since the valve experiences a pure free return in this portion of the response. 3.3.3 Closed-Loop Control Scheme Valve opening timing control can be achieved by compensating the identified solenoid 1 delay Atl at every cycle. Controller design in this subsection focuses on the valve lift and closing timing control. These involve the adjustment of 51 and 62. Closed-loop valve lift and closing timing control Since the estimated damping ratios are available due to adaptive parameter identification, the closed-loop valve timing and lift control scheme is developed based upon the identified parameters and the lift control algorithm is validated in simulation. The structure of the closed-loop controller with the parameter estimator is shown in Figure 3.6. The control goal is to let the plant output y track the desired input ydcsire and the desired closing timing. The nominal values of 510 and 620 are computed based on the estimated C f1 and C f2. They are the feedforward control signals to the system. The error between ymax and ydesire passes through an integrator and then adds onto the nominal 510. That produces 81 as a feedback signal to the system for valve lift control. The integral action is added to achieve the zero steady state tracking error and at the same time to reject the step type of disturbance. M510, 620) can be depicted as a function that converts 810 and 620 to the force input u. In the same manner, 52 is constructed as a feedback signal. This allows the closed- 54 loop controller to track the desired closing timing. K1 and K 2 are two closed-loop gains. The control system operates in an open loop using pre—determined 511. and 621. until the parameter identification algorithm converges, and then, switches to closed-loop control to minimize the tracking error. A detailed control scheme is presented in Figure 3.7. System Yref e U__. Gp(S) 9 e2 C4- ) tcref model A 8 A f1 " 510 1 or 81 u reference 81(Cf1) — i A ’—-* adaptive u(81,82) parameter C72 52(Cf2) 520 @52 or 521 estimator closed-loop valve lift and closing timing contrcl open loop control Figure 3.6. Closed-loop valve lift and timing control scheme inputs include valve displacement, solenoids 1 and 2 current feedback, and supply pressure Psupply' Desired outputs are valve opening crank angle, valve closing crank angle, and valve lift height. This diagram includes the adaptive estimator that identifies both C f1 and C f2, and an algorithm developed to detect critical points including maximum valve lift height, valve opening and closing locations and peak displacement. etc. These results are used by the following algorithm to identify Atl, A752, 51 and 62. These four parameters are used to generates De fA and De f B pulses. De f A and De f B are then converted to solenoid commands sent to the valve actuator. It is critical to provide a suitable adaptation window which determines the start and end of adaptive identification at opening and closing stages Moreover, the returning point at closing stage could be affected by a number of factors. It greatly depends on hydraulic latch performance. for instance, when the latch is released 55 displacment error ymax, valve (error etc plant system pomlnal 81 (on) feed back compute alignment of startlng and force input to actuator open Figure 3.7. Control scheme with parameter identification based on model reference adap- tation method 56 or whether there is certain oil leak in the latch. Inaccurate locations of the start point at opening stage and the return point at closing stage may cause instability of parameter identification. Algorithms were designed to allocate these locations automatically. This increases the robustness of parameter identification. The adaptive parameter identification algorithm is used to generate feedforward control signals. The feedback closed-loop control will be applied in real time to obtain the initial conditions close enough to the true values so that small adaptive gains can be used to acquire stability. Solutions of 510 and 620 In order to compute 510 and 69 analytical solutions need to be established. It was found -0» that the system damping ratio is between over-damped and slightly under-damped cases based upon the identified values. Therefore, two first order systems are employed to ap- proximate the second order systems for both opening and closing stages in the region of interest. The closed-form analytical solutions are developed based on the first order system. The formulas of computing 510 in terms of C f1 are provided by Equations (3.18), (3.19) and (3.20). (510 = (51 — (Ail - At?) (3.18) 2 a. 6 = —ln — 3.19 1 U (a - ymax) ( ) f0 (1' = A—,p — I) (3.20) where f0 = APP], + Acame) — (AP + Acap)Patm is defined by Equation (4.1). The formula of solving 620 in terms of C f2 is provided in Equation (3.21). 100 5,, 52 = n —— 0 Cf20 ymax + 6]) ) (3.21) In Equations (3.19) and (3.21), a is derived accordingly for three cases as follows: C 26, C} < 4K pM underdamped C 0’ = 716:0; = 4KpM critically damped —C +‘/CQ—4K A] f f p ,C2 > 4K1” overdam ed l 2M f P p 57 with Cf = Cfl at opening stage or Cf = sz at closing stage. Open-loop parameter estimation and closed-loop lift control simulation The adaptive parameter estimation algorithm was simulated for 40 cycles and the results are presented in Figure 3.8 and Figure 3.9. The system was simulated with 80psi air supply pressure, 5ms lag between the activation of solenoids 1 and 2, 100ms solenoid period (equivalent to 1200RPM) and 257725 solenoid active duration. Figure 3.8 shows that C f1 and C f2 converge to 80 and 85 respectively. Note that these values are the damping ratios set in the plant model which served as the control target for simulation purposes. The error between the model and the plant outputs converges to a set tolerance in less than ten cycles. Figure 3.9 shows that after 510 and 620 were evaluated with the solution based upon the identified C f1 and C f2, they converge to 5ms (top) and 3ms (bottom) approximately. The estimated 510 is close to the true lag (5ms) used in the plant, and 620 is also approached to the 3ms model plant closing duration. The closed-loop lift controller is validated in a 40 cycle simulation using the level two model. The simulation results are presented in Figure 3.10. The system was simulated with 80psz' air supply pressure, 5ms lag between the activation of solenoids 1 and 2 during the open-loop parameter identification period, 100ms solenoid period (equivalent to 1200RPM) and 25ms solenoid active duration. The desired valve lift ydem-m is 5mm. The top diagram in Figure 3.10 displays the valve lift converging to the 5mm set point with zero tracking error. It can also observed from the middle diagram that that the nominal control input 510 is estimated to be 3.6ms based on the desired valve lift. As displayed in the bottom diagram of this figure, the plant is operated in an open loop condition to achieve the parameter convergence in the first ten cycles. The closed-loop control input 81 dropped from its initial value to 3.68ms at the eleventh cycle. This indicates the beginning of the closed-loop control and the system detects the reference input at this point. In the next cycle, the valve lift was brought down to 5mm. This one cycle transient response is one of the design criteria. 58 Damping ration Cf1 Cf1 (N sec/m) G O 60o _35 i0 i5 20 25 $0 55 4o ’5‘ 5 x 10 Error at opening stage 2,50 a E‘ 2 ‘2‘ 2 Aw'so 5 1o 15 20 25 30 35 40 E Damping ration Cf; 3 1oor, ; 80.rfi.., ........ . ........ ........ r ......... ........ - " 6"a _35 1'0 1‘5 io 25 so 55 40 g E 5 x10 Error at closing stage : I---'-n 1 ; . . : g2 ; ; ; . . ; ; o' o 5 1o 15 20 25 3o 35 40 cycles Figure 3.8. C f1 and C f2 identification simulation with fixed valve operation at 1200RPM 59 Estimate of A and 0.04 w , flab r 5b, 0.03 - 0.02 - 0.01 — 81°(sec) o 5 i0 i5 20 is so 55 4o 520(596) A N U 4‘ o 5 i0 is in i5 50 55 40 cycles Figure 3.9. 510 and (520 estimation simulation with fixed valve operation at 1200RPM 3.4 Verification of Parameter Identification Conver- gence on Test Bench 3.4.1 Intake Valve Control System Hardware Configuration An Opal — RTTM real-time control system was employed as a real time controller for the hardware-in—loop bench tests. This system consists of two 3.2GHz CPU’S equipped with two 16 channel A/ D and D/A boards and one 16 channel digital I/O board. The communication between the two CPU’s is a high performance serial bus IEEE 1934 fire wire with the data transfer rate at 400MHz per bit. CUP #1 is used for engine controls and CPU #‘2 is dedicated for controlling the EPVA. 60 A A 510( sec) valve lift (mm) 61 ( sec) Closed-loop valve Iifta nd 3“ convergence (sec) Figure 3.10. Closed-loop valve lift control at 1200RPM 61 10 I l g l l I I I 5 -V +.._ L o 5 15 15 20 25 35 35 40 0.02 s T oo1_| E. o 5 15 15 20 25 35 35 40 x103 45 ~ ‘ « 4 ._ . -1 3'56 5 25 25 35 35 40 cycles 3.4.2 Intake Valve Actuator Driving Circuit The solenoid driving circuit was designed to amplify the signal from the D/ A outputs of the real time controller and to sense the solenoid current. The circuit is required to have a short solenoid release time and fast switching capability with low noise. The circuit was made of switching MOSFETs (Metal-Oxide Semiconductor Field-Effect Transistor) and NPN BJT (Bipolar Junction Transistors). 3.4.3 Evaluation of Parameter Identification Convergence EPVA bench tests were conducted using a cylinder head of 5.4 liter 3 valve V8 engine. 200 cycle data was recorded at different engine speeds. The convergence of adaptive parameter identification algorithm was verified using the bench test data. There are two sets of data equivalent to engine speed at 1200RPM and 5000RPM. At 1200RPM, the test parameters are 80psz' air supply pressure, 100ms solenoid period with 25ms solenoid active duration. The lag between the activation of solenoids 1 and 2 was 5ms. The parameter identification resulting at 1200RPM are presented in Figures 3.11, 3.12 and 3.13. Figure 3.11 shows that C f1 and C f2 converge to 55 and 65, where the error between model and plant outputs reduce to less than the given tolerance. Figure 3.12 displays 510 and 620 computed with the estimated C f1 and C f2. Both parameters converges to about 5.8ms and 3ms respectively and they are close to the true lag of 5ms and the measured return time of 3ms. The last cycle of valve response with the model response is displayed in Figure 3.13. The two rectangular windows are the parameter identification regions for opening and closing stages. The adaptive algorithm is inactive outside these two windows. The test parameters at 5000RPM are 801933 air supply pressure and 24777.3 solenoid period with 6ms solenoid active duration. The lag between the activation of solenoids 1 and 2 was 5ms. The parameter identification resulting at 5000RPM is presented in Figures 3.14, 3.15 and 3.16. Again, Figure 3.14 shows the convergence of C f1 and C f2. Figure 3.15 shows that 510 and 620 reach steady state values that are quite close to the true values. Figure 3.16 presents the 62 last valve lift with reference model outputs and the identification windows. I damping ratio Cf1 at opening stage 1 error between measured and model displacement at opening stage Cf1 (N secl ) 2: § AA; A AAA A v v O O ONO l l L error (m) )0 i3 . -'r E damping ratio Cf2 at closing stage E, 100 . . . m E 50 - ~ 9 0 error between measured and model :0 2 x 10‘3displacement at closing stage '- 0 o h 2 1 1 . ° 0 50 100 150 200 cycles Figure 3.11. C f1 and C 12 identification with 200 cycle valve bench data at 1200RPM 3.5 Closed-loop Intake Valve Control Scheme for Real Time Application This section presents the detailed closed-loop intake valve lift, opening and closing timing control schemes for the real time application. 3.5.1 Closed-loop Lift Control The architecture of the closed-loop valve lift control is depicted in Figure 3.17. System inputs include reference valve displacement, solenoids 1 and 2 current measurements from 63 x10"3 Estimate Of 810 and 520 A5 ................................. 3 £4L— .......................... O <52- 00 50 150 150 200 x10-3 520 (sec) o N 3s c» 0 50 150 150 200 Figure 3.12. 510 and 620 estimation with 200 cycle valve bench data at 1200RPM 64 Measured valve and model output in adaptation window 0.012 - - - mjdel output ‘ ------- model output 0.01» —— measured output . . . - — adaptation window 0.008 - » - I I 0.006 f , : I 0904- ~ 1 ~ - 5 '. a 0.002-~~ i . ' | 0 19.9 19.92 1941995 19.98 time (sec) 20 Figure 3.13. The last valve lift profile at 1200RPM with the reference model output 65 Damping ratio Cf1 at opening stage 50[| ................. ............... ................. ... 0 Error between measured and model a O O 011 (N sec/m) E 0 02 displacement at opening stage a o ..-- - I- - - 15-0321- 4 J i % Damping ratio Cf2 at closing stage a 5., El" ................ ............ g ........... g g 0 Error between measured and model E 2 X, fl? displacement at closing stage 3 ° ; _ ; t -2 . . . In 0 50 100 150 200 cycles Figure 3.14. C f1 and C f2 identification with 200 cycle valve bench data at 5000RPM 66 /\ _3 Estimate of 510 and 520 x 10 A 6 ..... 0 d) on ‘32 (co 2 00 50 1‘00 1'50 200 -3 x 10 A 6 0 0 3 4 ......... (8‘0 . 2 {r n _._ 1 L "0 50 100 150 200 cycles Figure 3.15. 310 and 620 estimation with 200 cycle valve bench data at 5000RPM 67 Measured valve and model output in adaptation window 0.012 - L - model output lllllll model output o_o1 . — measured output — adaptation window 0.008 ~ - . ’ 0.006 - 0.004L \ 0.002 - \ o ._._.I . ......... \ .1............. 4.78 4.785 4.79 4.795 48 time (sec) Figure 3.16. The last valve lift. profile at 5000RPM with the reference model output 68 the solenoid driving circuit (see Experimental Implementation section), air supply pressure, and oil pressure. The valve lift height is the output. The lift control consists of two parts, the open—loop parameter identification for feedforward control and the closed-loop lift control using a PI scheme. The system starts with a short period of open-loop valve operation where C fl is estimated using a high adaptive gain to achieve fast convergence. A subroutine checking the convergence of C f1 switches the system from open-loop Operation to closed-loop control as soon as the identification error stays below a given tolerance for a reference number of cycles. The open-loop identification period can take around 50 cycles. The open-loop identification scheme and the closed-loop lift tracking scheme are displayed in the upper and lower dotted line blocks respectively. The open—loop parameter identification scheme includes the plant, the model plant, and a driving circuit. The inputs of the driving circuit are the solenoid command pulses from the prototype controller’s D / A. The outputs of it are the amplified solenoid commands and the solenoid current feedbacks. Moreover, the parameter identification scheme comprises an algorithm that creates a C f1 identification zone where the adaptive algorithm is active and the displacement error is detected to be used by the adaptation law. The open-loop scheme also contains the model reference adaptive system involving the MIT rule with a high adaptation gain 71. The direct force input to the model plant is computed from the solenoid pulses by a subroutine. It guarantees that the model plant output starts at the same point as the plant output. These subroutines complete C f1 identification. Meanwhile, the De f A and De f B pulses are generated by a predetermined 511.. They are converted to two solenoid pulses amplified by the driving circuit for the EPVA actuators. In addition to the subroutines used in the open-loop parameter identification period, additional algorithms were developed for the closed-loop valve lift tracking control. There are algorithms that compute the feedforward nominal control input (310), detect system delay Atl and Atg and compute critical points including maximum valve lift, valve opening and closing locations, peak displacement, and so on. In this block, the model reference adaptive system (MRAS) uses a low adaptation gain '71 to maintain parameter convergence 69 due to a sudden change of the valve displacement in a transient operational condition. The feedforward nominal control input 510 calculated from C f1 needs to be sufficiently accurate to minimize the transient response time and the tracking error. The actual valve lift is a feedback signal to the system and it is subtracted from the reference valve lift to form the lift error. This error is the input of a proportional and integral (PI) controller with Kp as a proportional gain and K,- as an integral gain. The PI controller is updated every engine cycle. The output of the PI controller is then added onto the feedforward nominal input 510 to generate 51 as a controlled input to the system. The integral action is used to achieve the zero steady state tracking error. The De f A pulse is generated based on 81. The De f A and Def B pulses are converted into solenoid commands. They are amplified by the solenoid driving circuit for the valve actuators. As discussed in the Control System Hardware Configuration section, there are two CPU’s in the prototype controller. CPU#l operates at a relatively slower rate (1 ms) than CPU#2, but its outputs can be synchronized with the engine crank angle. CPU#2 is dedicated to valve operation at a sample rate of 40 microseconds since the valve con- trol algorithms require fast sample rate. The CPU#2 also takes care of the conversion from the De f A and De f B pulses to the solenoid pulses. The PI controller is operated per engine combustion event. It is implemented in CPU#I to reduce the computational throughput of CPU#2. De f A and De f B pulses are generated in CPU#l since they are crank synchronized. Closed-loop opening timing control In order to track the reference valve opening timing calculated by the engine control CPU#l, the valve control system needs to detect the magnetic delay of valve solenoid 1 Atl which is equivalent to the time lag between the activation of solenoid 1 and the actual valve opening. With known Atl, the control system can track the reference opening timing by compensating the delay Atl. The main task of this control scheme is the system delay detection and its closed-loop PI controller. The solenoid delay Atl is calculated using 70 solenoid 1 current obtained from the solenoid driving circuit. It is used as feedforward con- trol. The true valve opening timing is used as a feedback to the closed-loop controller, and it is subtracted from the reference valve opening timing to form an error signal of the PI controller. The output of the PI controller combined with feedforward control Atl produces the final control input to the engine control system which updates the De f A pulse. Most algorithms are implemented in CPU#2, except for the crank angle synchronized De f A and De f B pulse generation and the combustion event based PI controller that are implemented in CPU#l. Closed-loop closing timing control The closed-loop valve closing timing control and valve lift control schemes share the similar approach. Figure 3.19 shows the open-loop parameter identification for detecting C f2 and the closed-loop valve closing timing controller. The adaptive gain 72 is high in the open- loop operation and low in the closed-loop operation. A predetermined 62:. controls the valve closing timing in the open-loop operation. The system switches from open-loop to closed-loop control based upon the convergence criterion of the estimated C f2 which is the same as the opening case. The feedforward control 620 is computed from the identified C f2, and the system control output 62 consists of the feedforward control and the PI control output. Information from 62 is then used to generate De f A pulse. The De f A and De f B pulses are sampled by CPU#2 and converted to solenoid control commands that are sent to the valve driving circuit. Again, the PI control algorithm and the formation of De f A and De f B pulses are implemented in CPU#I, and the rest of the algorithms are implemented in CPU#2. The closed-loop timing control scheme allows the actuator to track the reference closing timing. 71 Ymodel detection In ID window Cf1 identification convergence check direct force input solenoid Figure 3.17. Schematics of closed-loop valve lift control 72 CPU#2 reference valve At2 I "1 Crank angle synchronized DefA and and DefB solenoid Figure 3.18. Schematics of closed-loop valve opening timing control 3.6 Conclusion In this chapter, a control oriented model called level two model was developed for model ref- erence parameter identification. This level two model is a piece wise linearized model based upon a previously developed nonlinear model which was built using Newton’s law, mass conservation and thermodynamic principles. The level two model reduces computational throughput and enable real time implementation. A model reference adaptive scheme was employed to identify valve parameters required to generate real time control signals. The convergence of adaptive parameter identification algorithms was experimentally verified us— ing the test bench data at 1200RPM and 5000RPM engine speed. Parameter convergence was achieved within 40 cycles. Error between the model and plant outputs were converged to set tolerances. Closed-loop lift control strategy was developed and validated in simu- lation. One cycle transient response and zero steady state tracking error was achieved in Simulation. The detailed closed-loop intake valve lift, opening timing and closing timing control schemes were presented. The closed-loop intake valve control algorithm will be evaluated by experiments in chapter 5. 73 CPU#2 '— sz does NOT converge Cf2 error I convergence check | Cf2 identification converge identification I Valve displacement detection synchronized with valve return - -int Y Plant measure Valve lift error lifl _. Model Ymodel detection [" plant in ID window ymeasure valve lift error lifl error I detection in D wimww ow adaptive gain 12 'a ve c os ng timin- detection closing timing error Crank angle synchronized DefA and DefB 52 Crank angle synchronized DefA and DefB —__._l reference valve closing timing with valve return Valve displacement detection synchronized int Figure 3.19. Schematics of closed-100p valve closing timing control 74 CHAPTER 4 Exhaust Valve Control System Development 4.1 Introduction The modeling and control of intake valves for the Electro—Pneumatic Valve Actuators (EPVA) was shown in early chapters and chapter 4 extends the EPVA modeling and control development to exhaust valves for both valve timing and lift control. The control strategy developed utilizes model based predictive techniques to overcome the randomly variable in-cylinder pressure against which the exhaust valve opens. 4.2 Exhaust Valve Dynamic Model A physics based nonlinear model, called a level one model, was built component-by- component based upon the flow and fluid dynamics. The details of the level one model and its verification can be found in chapter 2. This model provides an insight to the op— eration of the pneumatic/hydraulic mechanical actuation system. A piecewise linearized level two model was then created based on the level one model to reduce the computational throughput for control system development purpose. The details of the level two model are described in chapter 3. The level two model was used as the actuator model for the intake 75 valve in the previous studies. Here, it is used for the exhaust valve actuator modeling. The exhaust valve opens against a high in—cylinder combustion pressure with large cycleto-cycle variations. This in-cylinder pressure produces a force on the face of the exhaust valve that affects the valve dynamics. This in-cylinder pressure is modeled and integrated with the exhaust valve actuator model to capture the exhaust valve dynamics. The system dynam- ics illustrated here focuses on the relationship between the solenoid control commands and the exhaust valve response. It follows the same analysis as that of the level two model which simplifies the system dynamics used for the level one model analysis. As shown in Figure 4.1, the valve response can be divided into three stages. They are the opening stage (I), dwell stage (II), and closing stage (III). Solenoid #1 is activated at point 0 first. It induces a high air pressure force to push the valve open at point 1 after Atl. Solenoid #2 is then activated (point 2) with a time lag til. It removes this air pressure force Atz time after solenoid #2 is activated (point #3). Note that the interplay between two solenoids results in a pulse force input to the actuator valve piston with pulse width 61. The increment of the pulse width increases valve lift. Now, with zero input, the valve movement continues until it reaches its peak lift at point #4, the valve equilibrium. This ends the open stage. Next, the valve enters the dwell stage where it is held open by a hydraulic latch mechanism. At the end of the dwell stage, solenoid #1 is deactivated at point #5. After At3 time, the valve starts to return (point #6). The close stage starts at point #6 and ends at point #9 where the valve is considered closed. The returning duration is 62 between these two points. The two solenoids have electro-mechanical delays after their activation and deactivation (see Figure 4.1). Atl is defined as the delays for solenoid #1 at activation. Atz is defined as solenoid #2 delay at activation. The deactivation delay for both solenoids are At;;. The solenoid commands direct the valve motion after the delays. The time lag applied between the activation of two solenoids is denoted as 51. This differs from the time lag between two delayed solenoid activations which is denoted as 61 since two solenoid delays, Atl and Atg, are not equal. The exhaust valve lift control algorithm is to determine 76 EPVA Lift Profile Solenoids Activation Ill close |oplenI dvi'ell x | 3:22 5 16 l 7 0 , 4 8 9 131.551.5585“ “‘8 12 v N3 81 "’ W} 62 time T‘QSFPWN 7‘9 ‘09? solenoid #1 activated ' air pressure force on and valve opens solenoid #2 activated air pressure force off S1: solenoid #1 82: solenoid #2 M1: solenoid #1 turn-on delay At2: solenoid #2 turn-on delay At3: solenoid #1 and #2 valve peak displacement turn-off delay solenoid #1 and #2 deactivated valve returns without resistance valve returns against cmpressed residual air hydraulic damper activation : valve closes Figure 4.1. Valve lift profile with the solenoid command chart 77 when to activate solenoid #2 during exhaust valve opening for each cycle with the varying in-cylinder pressure at the face of the valve and its activation delay in presence. It is impossible to remove the input force Fa instantly upon the activation of solenoid #2 due to its activation delay. An model based predictive lift control algorithm is developed to make this possible. The details are described in the control strategy section. The exhaust valve closing timing control requires knowledge of 62, the amount of time that the valve takes to close. To guarantee the exhaust valve closing at the desired time requires deactivating solenoid #1 by time 62 before exhaust valve closing. 62 can be predetermined from the different valve lift set points. In other words, the closing timing control relies on a repeatable valve lift control. Developing a lift control system is the primary emphasis of work described in this paper. The opening stage exhaust valve actuator model and the in-cylinder pressure model are employed to formulate the model based predictive lift control scheme. In order to validate the exhaust valve lift control algorithm, the level two model integrated with the in—cylinder pressure model is used as a plant model in simulation. The opening stage exhaust valve actuator model and the in-cylinder pressure model are introduced in the following two subsections. 4.2.1 Actuator Model The opening stage exhaust actuator model with the in—cylinder pressure is studied in this section. This model is expanded based on the level two model from chapter 3 to include the in-cylinder pressure dynamics. Figure 4.2 shows the schematic diagram of the single actuating piston for this system. At the opening stage, the valve actuator is modeled as a second order mass-spring-damper system with zero initial conditions, see Equation (4.1). All pressures used in modeling and control formulation process are gauge pressure in this article. My + Cfg) + Kp(y + 61,) = Fa(t) — Fb(;r) (4.1) 78 oil POll Psupply Ain outlet port __I I I I inlet port Aou r . X 1 piston Mspring p -L Cf Kp I QLLL ? Mvalve F b(x) Figure 4.2. Actuator piston model 79 Fa“) = F“) _ F(t — 61) (4-2) 0 Ht<0 F“) = ’ . where, Pp = Pail z Psupply» and — Fb(:r) is the in-cylinder pressure force at the back of the valve modeled in the next section; - M = Mpziston + Mvalve + 35M spring + Mcap, where Mpz'ston is the mass of the actuator piston, Mvalve is the mass of the intake valve, 1W spring is the mass of the valve spring. The effective spring mass equals one third of the total spring mass [15], and Mcap is the mass of the cap on the top of the valve stem; - Ap = 7rr12, —— mg“ and A0,) = 777%“ with rp as the radius of the actuator piston and rm) as the radius of the oil passage; - C f is the damping ratio approximating energy dissipation due to flow loss and fric- tional loss; — KP is the stiffness of the valve spring; - (5,, is the preload of the valve spring; - PI) is the iii-cylinder air pressure, P0,) is the oil pressure and is at the same pressure as air supply, and Psupply is the air supply pressure; - Amp is the area of the cap on the top of the actuator piston stem; - 61 is the lag between the activation of solenoid #1 and solenoid #2 after solenoid delays as illustrated in Figure 4.1, and 62 is the time needed for the valve to return to the seat. 80 x |—‘ Tatm . Ii’atm m valve mcyl Tcyl Pcyl Acyl cylinder piston Figure 4.3. In-cylinder pressure model 81 4.2.2 In-cylinder Pressure Model The in-cylinder pressure Fb(2:) needs to be modeled and evaluated in Equation (4.1). F ig- ure 4.3 illustrates the dynamics in the combustion chamber with an exhaust valve. A control volume is drawn above the piston, where mcyl, Tcyl and Pcyl are the mass, temperature and pressure inside the combustion cylinder. Acyl is the engine piston area. men; is the mass flow rate at the exit when the exhaust valve opens. Tatm and Patm are the atmospheric temperature and pressure. .2: and y are the exhaust valve displacement and cylinder piston displacement respectively. The mass flow rate equation at the exit are written for both choked and unchoked flow cases through Equations (4.3) to (4.5) following their derivation in [7]. __’°_ RT 1 cy Them = Cdex'ypcylAexCC) , A31) : 27rrvalve$ (4.3) where, A33; is the flow area with rvalve being the valve radius; Cdez is the flow coefficient at the exit; R is the residual gas constant. 0,, and CU are the specific heat of the residual . C gas at constant pressure and constant volume respectively and k = :5. When Pay; 2 k (kg—HkZ-lpatm, the flow is choked at the exit. In this case, 7 is shown in Equation (4.4) k l 7 = ,hfipfi—i. (4.4) I: When Pcyl g (kg—IVF—TPatm, the flow is unchoked and '7 is expressed in Equation (4.5) 2 Patm bi; Patm 1_k = -— 2' —- ‘ —1. 4. 7 hype“) [( 13.,le 1 < s) The mass of the residual gas inside the combustion cylinder in Equation (4.6) can be obtained by integrating the calculated mass flow rate. The initial mass m0 is derived using ideal gas law, where P0, V0, R0 and Tcylo are the initial in-cylinder gas pressure, volume, gas constant and temperature at the exhaust valve opening. 82 Using the ideal gas law again with the obtained moi/1 results in an expression of in-cylinder pressure as shown in Equation (4.7). m'cyl RTQI/l Pcyl = TV Vol/l = Acyly- (4'7) cyl where, k, R and Tcyl are variables acquired from the WAVETM simulation with the same engine configuration and parameters; and y is the piston displacement derived from the cylinder geometry in Equation (4.8). L L y = r[1 + ; -—— cos(6) — ; — sin2(6)] (4.8) - Acyl = 776 x bore)2 = 0.04017712 (bore = 90.2mm) L is the connecting rod length (L = 169.2mm) r is the crank shaft radius (7" = admire = 52.9mm) 6 is the engine crank angle. Therefore, Fb(.r) can be expressed in Equation (4.9) below. Fbiir) = Pct/(Avalvc’ (4'9) where Paul is defined in Equation (4.7). 4.2.3 Validation of In-cylinder Pressure Model by Simulation The in-cylinder pressure force Fb is a function of the exhaust valve displacement since the flow out area Am is a function of the exhaust valve displacement. In order to validate the in-cylinder pressure model, combustion experiments were conducted using a 5.4L 3 valve V8 engine with in-cylinder pressure measurement and a conventional cam shaft at 1500RPM. The pressure model was simulated using the conventional cam profile as the valve displacement input. The modeled in-cylinder pressure was then compared with the measured in-cylinder pressure as shown in Figure 4.4. The top diagram of this figure shows 83 the modeled pressure (solid line) in the rectangular windows and measured in-cylinder pressure (dash line) with satisfactory modeling accuracy. The bottom diagram shows the exhaust cam profile used in the simulation and experiments. The in-cylinder pressure model Measured and modeled cylinder pressure with cam profile at 1500RPM A 3 x106 .1: ' —W saw v mo 9 rassure 3 2 -------- measu e pressured lCl 'o 5 1 - E I! n.” 0 Cam profile i 0.01» .2 a o a 0.005- E 8 0 cycle Figure 4.4. In—cylinder pressure model validation by simulation is then integrated into the pneumatic exhaust valve model and the responses are shown in Figure 4.5. Here, the pressure model uses the EPVA valve displacement to calculate the corresponding in-cylinder pressure. The modeled pressure (solid line in top diagram) and the associated EPVA valve lift profile (solid line in bottom diagram) are compared with the experiment pressure (dash line) and the cam profile (dash line). The simulation result demonstrates that the in—cylinder pressure drops rather quickly with the EPVA exhaust valve actuation since the EPVA valve opens faster than the conventional cam based valve. This simulated iii-cylinder pressure is used to construct the control signals. The exhaust valve model is used as a plant model and it is integrated with the in-cylinder pressure model in simulations to validate the control algorithm. The modeled in-cylinder pressure is one 84 of the two inputs to the plant (exhaust valve) and the actuation force Fa commanded by the two solenoid control signals is the other input. Measured cylinder pressure with cam pro rofile and model cylinder pressure with EPVA lift profile at 1500RPM A 6 E 3 x10r . t 1 . . 1 :3“. ‘ gu'Pcam l 2 — cyl .- lg . «I 1 L 5 ~ ‘ ‘ 0.0 o M. CAM profile and EPVA lift profile "cam and x (m) : '. L ’ . j I ‘ ‘ 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 time (sec) Figure 4.5. In-cylinder pressure model integrated into exhaust valve model 4.3 Control Strategy Since the in-cylinder pressure on the face of the exhaust valve varies significantly from cycle to cycle, the valve lift control needs to be adjusted as a function of the current in- cylinder back pressure for each individual cycle. As explained in the actuator dynamics section, the exhaust actuator is modeled as a second order mass-spring damper system at the opening stage. Activating solenoid #1 applies the force Fa on the valve and moves the exhaust valve. Activating solenoid #2 removes the force and the valve continues to open until it reaches the maximum displacement. Solenoid #2 activation timing determines the 85 maximum valve lift. Therefore, the key for valve lift control is to find when to activate solenoid #2. Figure 4.6 illustrates the idea of the exhaust valve lift control strategy. Solenoid #1 is activated at time 0. After the delay of Atl, the input force Fa acts on the system and the exhaust valve starts to open at point 1. Solenoid #2 is then activated at point 2, after Atg delay, force Fa is removed at point 3. The valve moves further until its velocity decreases to 0 at point 4. The second order valve system response from points 3 to 4 can be calculated with zero input and nonzero initial conditions at point 3. In other words, the valve peak displacement at point 4 can be calculated if the initial displacement and velocity at point 3 are known. Once the calculated displacement at point 4 reaches the reference maximum valve lift, point 3 is found to be the right time to remove force Fa. If activating solenoid #2 could turn off the input force Fa immediately, we would only need to activate it whenever the calculated displacement of point 4 reaches the reference lift. But the solenoid delay requires the activation to take place at point 2 with Atg amount of time before point 3. This means that if point 3 is the time to eliminate input force, point 2 is the time to activate solenoid #2. However, the initial conditions at point 3 where the peak displacement of the valve is calculated are not yet available at point 2. Therefore, an algorithm is derived to predict initial conditions of point 3 at point 2. This strategy of initial condition prediction can be implemented as long as the delay Atg of solenoid #2 is less than the lag 81 between the activation of two solenoids. The predictive algorithm needs to know both states, valve displacement and velocity, at point 2. An Kalman state estimator was used to estimate them with minimized effect of measurement noise. Now we can determine the time to activate solenoid #2 (point 2), which is served as a feedforward control of the valve actuator. A PI scheme is used as a feedback closed—loop lift control system to reduce the steady state lift tracking error. The flow chart of the feedforward control scheme is shown in Figure 4.7. First, the solenoid #1 is activated. Secondly, the Kalman state estimator provides the current states. Finally, a model based prediction algorithm uses the estimated states to calculate the states after solenoid #2 delay Atg, which is then used to calculate the peak valve displacement. If 86 (X(tp)=Xmax, 51(19):» 5 5 Peak Displacement Calculation 3 llnitial Fa Condition 5 . Prediction 2 E (X(td)=Xo 1 xltdl'VO) Kalman Filter (x=2 , i=2) 0- 1 a a ; (xao , )'(=o)E Lg Etp time 323: —.I . At1 j _| |_A_t2 At3i rrn'e 12v S AAVIIII J $1: solenoid #1 $2: solenoid #2 M1: solenoid #1 turn-on delay Atz: solenoid #2 turn-on delay At3; solenoid #1 and #2 tum-off delay Figure 4.6. Exhaust valve lift control strategy 87 the calculated peak displacement is greater than or equal to the reference valve lift, solenoid #2 is activated, otherwise, the process repeats until the condition is satisfied. The details of the derivations are discussed in the following four subsections. 4.3.1 Peak Displacement Calculation (PDC) This section describes the solution for the peak displacement at point 4 based on the initial conditions at point 3. Recall that the governing equation of the exhaust valve at the opening stage is presented in Equation (4.1). The back pressure force Fb(:r) equals the product of the exhaust valve area and the modeled in-cylinder pressure. The in-cylinder pressure used in the control algorithm development here is piecewisely linearized according to the simulated in-cylinder pressure against EPVA exhaust valve profile as shown in Figure 4.8, where Fb(1:) = p3: + q (p S 0 and q > 0) with P = P1. q = q1, x g 0.002m P = P2. 0 = Q2. 0.002m < :1: g 0.008m P = P3, q = (13, x > 0.008m Substituting Fb(17) with its linearized expression in Equation (4.1) results in Equa- tion (4.10) below. Mi+ij3+Kpr=Fa—(px+q)—Kp6p (4.10) Move the pa: term to the left resulting in Equation (4.11): Let K = K p + p and Fa = 0 since it is assumed that input force Fa is turned off to obtain Equation (4.12) in a general format given the initial condition 27(0) = .130, :i:(0) = 120. Jili+Cfit+Kx= -Q, Q=Kp6p+q (4.12) Recall that p takes three different values. p1, p2 and p3 in three valve displacement regions. K could be either negative, zero or positive depending on the value of p. When K is positive, Equation (4.12) can be rewritten into Equation (4.13) as below: 5: + 2Cwnj: + .531: = —% (4.13) 1 88 Feed forward exhaust valve lift control scheme in one engine cycle P » Activate solenoid #1 i Current state estimation using Kalman filter 1 Model based state prediction for the delay of solenoid #2 1 Peak exhaust valve displacement Xmax calculation I10 Xmax 2 Xref ? Activate solenoid #2 l End Figure 4.7. Feedforward exhaust valve lift control strategy 89 Piecewise linearization of back pressure force for the model based predictive control ck N 0| 0 0.506 0. 03 0.01 0 0.502 0.004 valve lift (mi Figure 4.8. Piecewise linearization of iii-cylinder pressure 90 , C where wn = V 1%] and C = —2£(/ 3717;. In this case, the solution can be categorized into un- der damped, critically damped and over damped scenarios depending on the value damping ratio C, damping coefficient C f, mass M and equivalent stiffness K in Equation (4.13). The peak displacement solution derivation of Equation (4.12) proceeds separately in four cases. Case#1isK>0with00withC=1,case#3isK>0with C > 1 and case #4 is K S 0. The initial condition denoted as 97(0) = 51:0 and 23(0) = no in this section are derived in the next section of model based initial condition prediction. PDC case #1 K > 0 with 0 < C < 1 (under damped) We start with solving Equation (4.13) for all three cases where K > 0. The homogenous solution 33h can be expressed in Equation (4.14) 93h = e—Cw’ltmlewdt + age—wdt), wd = V1 — C2wn (4.14) Solving for the particular solution 13,, of Equation (4.13) results in Equation (4.15) 13p = —% (4.15) The complete solution r(t) = Ip(t) + rh(t) can be expressed in Equation (4.16). 1,“) = 6—Ctdnf(aleiwdt + a2e—iwdt) _ % Applying Euler formula em = cos(a) + isin(a) and trigonometric identities to the equation above to obtain Equation (4.16) 13(1‘) = Ara—(“mtsinwdt + 19) — g (4.16) where A and 6 are determined by the initial conditions as follows: 33(0) = Asin(6) — 7? = $0 27(0) = —CAwn sin(9) + w(1.4cos(6) = no (‘ir'()+CwnX0)2+X2~U2 A=\/ 2 0‘1.X0=170+% OJ d = , -1 _‘*’cL‘£L_ 9 tan (19()+CW'7IX()) 91 The peak displacement '13,, = :1:(fp) is solved at :i:(tp) = 0 with tp being the time the valve takes to travel to its maximum displacement (see Figure 4.6). Taking the time derivative of .1:(t) and setting it to zero at tp result in Equation (4.17). $0,) = -CwnAe CW" ‘Psin(w adtp + 9)- _ 0 (4.17) Solving Equation (4.17) yields: t—1 1_ _ —1 1_ (an ( 7 ) 6), tan ME? 1>9 t. = p (tan’1( €12 —- ) — 9 + 27r), otherwise :EIHEIH T? Substituting tp into Equation (4.16), we obtain the peak displacement 22(tp). The solution of the peak displacement is summarized below: r PDC Summary K > 0 with 0 < C < 1 J $(tp) = Ara-Cui'ltf sin(w:tp + 6)— fix U +CW7iX0 7131(th 1( __12_ 1)—0),tan-1,/C1-1>9 —(l.an 1( J?— 1)- 0+27r),0therwise 2 g _ (10+CW71X0)2+X() , _ —.‘L‘() + 1% W12: \/][i1[9=E:Z\/mraWd—— V 1 — C2W'n 1‘0 = 17(tdlv vo— ‘ 430d) 17(td) and :i:(td) obtained from tp: wd 4— model based initial condition prediction PDC case #2 K > 0 with C = 1 (critically damped) Again, the homogenous solution 17h and non—homogenous solution xp are shown below. rh(t) = (a1 + (1206—1127;! (4.18) The total solution is .r(t) = 1:},(t) + :irp(t) = (a1 + a.2t)e_w"t — % (4.20) 92 where a1 and a2 below are obtained by evaluating the above equation at the initial condi- {5:504 (12 = M) + wn('170 + %) Similarly, we solve for tp and 13(tp) at 23(tp) = 0. The expression of peak displacement tions 13(0) = 2:0, i‘(0) = 110. 27(tp) is summarized below: [ PDC Summary K > 0 with C = 1 I map) = (a1 + a2tp>e‘“’"tp - % (4)1102 €11=I0+1Q\-102=vo+w72($0+%),wn=Vii} 130 = 330(1), ’00 = 930(1) 112(td) and :i:(td) obtained from model based initial condition prediction PDC case #3 K > 0 with C > 1 (over damped) The homogeneous and non-homogeneous solutions of Equation (4.13) in this case takes the following form, :rh(t) = aleAlt + ageAQt where /\1 = —Cwn — tam/C2 — 1 and A2 = —Cwn + cum/ C2 - 1, '13,, = —%. (4.21) The total solution is shown in Equation (4.22) w) = rh(t.) + spa) = aleAlt + ageizt —% (4.22) Evaluating the total solution at the initial conditions 1:(0) = :50, 15(0) = no results in a1 and a2 as below: _ _,,,0+(_C+ C2-1)wnxo 2.0,, (2—1 vo-i-(C-i- C2-1)wn X0 2wn\/C2—l (12: 93 Solve for tp at 22(tp) = 0 to obtain: 1 —A a tp:{ mini—21,51, a1a2A1A2 <0 no solution, otherwise Evaluate 22(t) at tp to obtain the peak displacement 23(tp). The solutions are summarized below: [ PDC SummaryK>0withC>1 $(tp) = alexltp + age’VtP — g —A p . . no solutzon, othermse a1 _ -v0+(-C+\/C2-1)Wn)(0 a2 = v0+(C+ C2-1)wnxo mum/<24 ’ mum/<24 )‘1 = _CWn ‘WnVC2 - 1, ’\2 = ‘CWn‘l'WnVC2 '1 C Lana/ii, Cali/171:; $0 = $(td), v0 = 5530(1) a:(td) and :i:(td) obtained from model based initial condition prediction PDC case #4 K S 0 The homogeneous and non-homogeneous solutions of Equation (4.13) with K S 0 takes the form in Equations (4.23) and (4.23). 3W) = 0162“ + 026”, —C +‘/C2—4MK —C +‘/C2—4MK where A1 = f 2.4; and A2 = f 2Mf with c2 —4KM > 0 since K S 0. The complete solution is expressed in Equation (4.24). The coefficients a1 and a2 are provided in Equation (4.25) by evaluating Equation (4.24) at the initial conditions 93(0) = 1:0, 35(0) = '00. a:(t) = xh(t) + :cp(t) = aleAlt + ageA2t — 1463— (4.24) 94 A2X0 - P0 ’00 - Alto (11: _ (12: Ag—Al’ A2~A1 Similarly, solve for tp below at Li:(tp) = 0: with X0 = 1120 + otherwise 1 —/\ a tp = { A2-X1 1n X202 ’ ala2/\1)‘2 < 0 no solution, K (4.25) Substitute the above solution into Equation (4.24) to obtain the peak displacement a:(tp) which is summarized below: [ PDC Summary K < 0 :1:(tp) = aleAltP + ageAQtP — 76% Q=Kp6p+q, K=Kp+p no solution, otherwise 1: 211 PP PF” :10 = 170d) 1’0 = 3i30d) :c(td) and :i:(td) obtained from 1 1n_’\1al (ta/\A <0 altpz{ Ag—Al A2(i2’ 1212 A —v =5§971102 2 A1 X0=$0+if —C + C —4AIK —C —4ll/IK f \/ f2 9,2: f W3 02 model based initial condition prediction 4.3.2 Model Based Initial Condition Prediction (ICP) The previous section solves for the peak displacement :i:(tp) using the displacement and velocity at point 3 as initial conditions (Figure 4.6). This section derives the formulas to predict the displacement $(td) and velocity :i:(td) at point 3, given the displacement and velocity at point 2. The displacement and velocity at point 2 are initial conditions denoted as 17(0) = :50 and i(0) = 120 in this section. Their values are estimated by the Kalman state estimation described in the next subsection. Solenoid #2 delay, Atg, is the time input and Fa is a constant force input between points 2 and 3. Consider the governing equation again in Equation (4.1). Given F‘b(1?) = p17 + q. Equation (4.1) becomes (4.26) Rearrange the equation above to obtain Na? + Cfi: + (Kp + 19)]: = Fa — q — Kprip (4.27) Let K = Kp + p and W = q + Kpdp — Fa, Equation (4.27) becomes Equation (4.28). A1325 + ij: + K1: = —W (4.28) It is clear that Equations (4.12) and (4.28) have the same form. Previously, Equa- tion (4.12) was evaluated for the maximum displacement. given initial conditions. Now, Equation (4.28) is evaluated for the displacement and velocity in td amount of time given initial conditions, where td = Atg (see Figure 4.6). The displacement solutions of Equa— tion (4.28) are the same as those of Equation (4.12) by replacing Q with W. The time derivative of the displacement yields the solution of the valve velocity. Similarly, the solu— tions can be categorized into four cases. They are under damped, critically damped and over damped with K > 0 and K S 0. The solutions are summarized case by case in the following subsections. ICP case #1 K > 0 with 0 < C < 1 (under damped) F ICP Summary K > 0 with 0 < c < 1 j $(td) = Ara—(”Md sin(wdtd + 0) — I}? if(td) = —CwnAe-C“’"td sin(wdtd + 9) +Awde-Cwntd COS(wdtd + 9) W = q + Kp5p - Fa» K = Kp +P .. 2 2. 2 A = \/(120+CwnX0) +X0wd, 9 = —tan‘1( win) ) a}?! ’lv’O‘l'CWn X0 W X0 = 170 + 77 .» C ”P: VRA7~C:72£\/171F’wd: ““42”" 51:0 = E, vO = :1? if and 3? obtained from Kalman filter state estimation 96 ICP case #2 K > 0 with C = 1 (critically damped) [ ICP Summary K > 0 with c = 1 1 90011) = (01 + aQtdle—wntd - W $011) = (126—“”7“" - (01 + a2tdlwne_“’"td 5’57—q+h’p6p‘F(l, K=Kp+p a1=10+ {a 02 =v0+wn('r0+7;) Wn = {‘7 1130: 15,110: x E and :1? obtained from Kalman filter state estimation ICP case #3 K > 0 with C > 1 (over damped) ICP Summary K > 0 with C > 1 I $(td) = aieiltd + a?2td — 5 5:.(td) — allleAltd + agAgeAQtd W=q+Kp5p— Fa, K: Kp+p a -'i;0+(—C+(/(2—l)wnx0 a2 v0+((+ <2_1)wnxo 1 = 3 4 = 2Wn\/C2—1 2Wn\/<2—1 A1: _CWn.’WnVC21-/\2= ’CWn‘i‘WnVCQ—l Wn = \/—1 C: _§[Vm x0=x, 110:2: if and Ti obtained from Kalman filter state estimation ICP case #4 K S 0 L ICP Summary K S 0 _ )‘ltd thd _ IV 37(td) - ale + age 7? i‘(td) = a1/\18’\1td + a2,\23’\2td W=q+Kp6p—Fa, K=Kp+p A , —' —/\ 01 = WY- v a a2 = v&2_k’: —C + C —4]WK —C — —41VK f V f A f V Cf )‘1 = 2M 1 2 — 2M 1 C X0=$0+ifii Wn=\/T[ (=1: m 230:2}, 110:2: 35 and :73 obtained from Kalman filter state estimation 97 4.3.3 Kalman Filter State Estimation (KFE) The displacement and velocity at point 2 (see Figure 4.6) are needed as initial conditions in the previous section. The system is equipped with a displacement sensor which measures the exhaust valve displacement. The velocity obtained through taking a time derivative of the measured displacement is unreliable due to the measurement noise. The observer formulated in this section performs the optimal estimations of both the displacement and velocity at point 2 in the presence of noise using Kalman state estimator. The estimated displacement and velocity are denoted as if and 513 respectively. The state space notation of the system is expressed below: if = Ax + Bu + Gw(t) y = C3: + v(t) 0 1 0 $1 whereA= -—C ,3: ,C=[10]andx= ;w(t)andv(t) 315 7171 1 “”2 represent the process noise and measurement noise. Note that u = —W is the input to the system, 271 = 2: and 2:2 = :i: are the states representing the valve displacement and velocity. The Kalman state estimator takes the following forms: $=AE+Bu+L(y—c§?) y=C§3, 313(0)=0 l . . . . . . where L = l1 ] is the observer gain acquired through solvmg the Algebraic Riccati 2 Equation (4.29) and Equation (4.30); and 5? = f1 ] contains the estimated states with $2 .751 and 52 being the estimated displacement and velocity. Note that G is considered as an identity matrix. AP + PAT + GWGT - PCTv-ICP = 0 (4.29) W20 and V>0 where W and V are covariance matrices of w and v, respectively. If (C, A) is observable, the Algebraic Riccati Equation has a unique positive definite solution P, and the estimated 98 state :3? asymptotically approaches true state :i: using L given by Equation (4.30). L = PCTV“1 (4.30) The estimator is summarized below with obtained l1 and [2: [ Kalman filter state estimation summary J 351= 52 + l1(1'31 - 551) x A CA A I2= -{V{1$1-7i{$2+fi+l2($1 --1‘1) 4.3.4 Closed-Loop Control Scheme The feedforward solution of solenoid #2 activation timing is obtained by implementing the formulas from the peak displacement calculation, model based initial condition prediction and Kalman filter state estimation subsections. This solution combined with the displace ment error compensation from the proportional and integrator (PI) feedback scheme forms a closed-loop control signal of solenoid #2 as illustrated in Figure 4.9. Closed-loop exhaust valve lift control scheme Feed forward —-> . control Signal Xref , © I Plant Xmax PI model P Figure 4.9. Closed-loop exhaust valve lift control scheme 99 4.4 Simulation Result The developed control algorithms are validated by simulation using the combined valve actuator and the in-cylinder pressure model as the plant model. The three segments of the feedforward control strategy and the closed-loop control scheme are evaluated in sequence. 4.4.1 Simulation of Peak Displacement Calculation Figure 4.10 demonstrates the simulation results in four out of 80 cycles where the solenoid #2 is activated when the calculated peak displacement reaches the reference valve peak lift of 11mm. This tests the open loop feedforward peak displacement calculation algorithm. The model valve displacement and velocity are employed as the known initial condition in this simulation. The top diagram shows that the peak valve lift is maintained at 11mm, rejecting the in—cylinder pressure variation at the back of the exhaust valve (shown in the bottom diagram) when the feedforward peak displacement calculation is applied. 4.4.2 Simulation of Model Based Initial Condition Prediction Figure 4.11 presents the simulation results of the model based displacement prediction. The solenoid #2 delay (Atz or td) is assumed to be 2ms in the simulation. White noise is injected to the plant displacement output to simulate the measurement noise. The plant displacement (solid) without measurement noise injected and the predicted displacement (dash) in the prediction active region are displayed in the top diagram for one cycle. The middle diagram displays the error between the two. The bottom diagram shows the error between the plant and predicted displacement of 80 cycles closed-loop lift tracking simu- lation with lift set points of 11mm, 6mm, 8mm and again 11mm. The absolute error is less than 0.7mm. The simulation results of the model based velocity prediction are shown in Figure 4.12. The absolute error between the plant and predicted velocity is less than 0.25m/s in all 80 cycles simulated using the closed-loop lift tracking control with four lift set points. 100 Valve lift control based on feedforward solution assuming no solenoid delay x(L005. .. 4...... . 6 g 10 Back pressure varying at the exhaust valve opening time 2.. g 1.57 a? 1 0.51- 01 Figure 4.10. Simulation validation of feedforward solution without considering solenoid #2 delay 101 error (m) valve disp. (m) error (m) _3 Valve dis lacement _of EPVAm ode l x 10 and 2ms predic' we model“ in one cycle at 1500RPM 10L _ ' a ' ' I I 1 ' o _1 ._.. I- _ - _. ___________ . . 0.08 _4 0.09 0.10 0.11 0.12 0.13 0.14 5X 10 Displacement error in one cycle 0 . V . . _5__ , . . . . . . . .4 time( (sec) 5x 10 Displacement error in 80 cyc es with 4 lift setpoints 0 _5 . . . . . . ., . . 3 ..... , _10 l i J i i l i 10 20 30 40 50 60 70 80 cycle Figure 4.11. Simulation validation of displacement prediction 370,, 102 1:3 BO 45 Valve velocity of EPVA model and 2ms predictive model in one cycle at 1500RPM 0.08 0.09 0.10 0.11 0.12 0.1 3 0.14 error (mls) valve vel. (mlsec) error (mls) Velocity error in one cycle 5% fl ....... .- .. ._ _ . time’sec)_ Velocity error in 80 cyc es with 4 lift setpoints _ ._. ... .._. .. ; . .. ' . . , . . ..Q. N. l II.III .I'Ia I'lllnf - l .1. -.II II ll.lllillli! IIII.IIII..III.IIPI.IIII ll _ll'llllll'lll ‘ "l';|"|'|' 'll""l . I j". I l I I If" 'lll'l'llll'|‘|'_',l". 10 20 30 40 50 60 70 80 cycle Figure 4.12. Simulation validation of velocity prediction :50}, 103 4.4.3 Simulation of Kalman Filter State Estimation Figure 4.13 displays a simulated valve displacement output with white noise measurement. Figure 4.14 and Figure 4.15 present the simulation results of the Kalman filter state estima- EPVA model displacement with measurement noise injected at 1500RPM 0.012 : . A 0.01» s g 0.008~' 8 x 0.005-~ '0 5 0.004- - x 0.002 0 ’ L L 3a ‘ 0.08 0.09 0.10 0.11 0.12 0.13 0.14 time(sec) Figure 4.13. Model displacement with measurement noise injected tion with the measurement noise in presence. The absolute error between the displacements of the plant (without measurement noise) and the Kalman estimator is less than 0.3mm. The absolute error between the plant velocity (without measurement noise) and the es- timated velocity is less than 0.38m/s. These comparison were accomplished in 80 cycle simulation using the closed-loop lift tracking control with four lift set points. 104 error (m) valve disp. (m) error (m) Model displacement and state estimation with measurement noise in one cycles at 1500RPM 0.01- .. T “,4. . ‘ ' x , ---2 0.005,........ . _ 00.0g .4 0.09 0.10 I 0.11 0.12 0.13 0.14 X 0 Displacement error in one cycle at 1500RPM 2 _ , . . I .. 0 ~-‘ _2_ ........ V._ ........................ . .4 -4 l tim5(sec) I X 10 Displacement error in 80.cycles with 4 lift setpoints 2 ...... a 0 I _ -2 ~ . S _4 l L M 1 i L 10 20 30 40 50 60 70 80 cycle Figure 4.14. Simulation validation of kalman filter displacement estimation 350 with mea- surement noise 105 error (mls) valve vel. (mls) error (mls) Model velocity and state estimation with measurement noise in one cycles at 1500RPM 4 w , - - . g— l I‘VA' _. _ .zt V l / V l: _ 4L , . - I “g x - 0.08 0.09 0.10 _ 0.11. 0.12 0.13 0.14 0.2 Velocity error In one cycle -0.2- V1 4 '0.‘ l l l time(s error in 80 c cles ew)ith 4 lift set oints Figure 4.15. Simulation validation of Kalman filister velocity estimation $0 with measure- ment noise 106 4.4.4 Simulation of Closed-Loop Exhaust Valve Lift Tracking Finally, Figure 4.16 presents the entire closed—loop lift tracking simulation result with all three feedforward control sequences assembled at four reference lift set points in the presence of measurement noise. The dark and grey lines in the top diagram represent the reference and model valve lift respectively. The bottom diagram demonstrates that the absolute lift tracking error is below 0.6mm at steady state. The exhaust valve tracks the reference lift within a single engine cycle having the lift error less than 0.5mm. Closed-loop valve lift trackgin with 4 lift setpoints at 1500RPM -3 x10 A12 l I I l l I E, hm... I —model valve lift Us“ _ - 9310— - - —referencevalvelift - ~ g 8 _ “wr'fiI’”.-m'1 _ E > . III—(\- n“ 6 — 1 ,_ . Displacement error in 80 cycles with 4 lift setpoints x 10 I I I 5 error (m) Figure 4.16. Simulation validation of closed-loop exhaust valve lift tracking control system with four set points 107 4.5 Real Time Exhaust Valve Lift Control Algorithm In this section, the closed—loop lift control strategy was evaluated by experiments. The feedforward lift control inputs were calculated before the real time implementation to save the real time throughput. The damping ratio of the exhaust valve model at the opening stage is need in constructing the feed forward lift control signal using the developed model based predictive lift control strategy. To identify this model parameter, the open loop lift control tests were conducted on the exhaust valve at 600RPM. The maximum pressure at the back of exhaust valve was set to be 60psz', the supply air and oil pressure was 120psz' and the target lift was 10mm. The valve back pressure varies randomly from cycle to cycle with the variation as large as 14.5psz'. The measured valve back pressure was used in the exhaust valve model simulation. The lag between the activation of two solenoids were kept the same in both the experiments and the simulations for parameter identification purpose. The experiment and simulation valve responses are displayed in Figure 4.17. The bottom diagram shows the model (dot line) and the measured (solid line) valve lift profiles in five cycles. The top diagram shows the corresponding pressure against with the exhaust valve opens. The damping ratio was chosen so that the model valve responses agree with the experimental valve responses as demonstrated in this figure. The developed model based predictive control strategy can be used to seek the timing of activating the second solenoid and use this timing as a feedforward lift control input in real time. In order to reduce the real time computational throughput, the developed strategy was used to calculate the lag between the activation of the first and the second solenoid for different lift set points in simulation. In the real time application, this lag was the feedforward lift control input which was combined with the feed back PI compensation to form a closed—loop lift control input. The measured valve back pressure in the pressurized chamber was piecewisely linearized and used in the feedforward control input calculation. The measured pressure was multiplied by the area of the exhaust valve to obtain the pressure force acting on the back of the valve. This force were plotted in Figure 4.18 (grey 108 EPVA Model Identification using pressurized chamber x105 pressure (Pa) Chamber O ) P o 3‘ i o_oo4_....§.._. ”1,“... cycle m f displacement Valve Figure 4.17. Exhaust valve model identification with measured randomly varying valve back pressure 109 curves) against the valve displacement for 20 cycles. As shown in this figure, they were linearized in three segments (solid lines) during the exhaust valve open to approximate the mean value of these forces. The coefficients, p1, q1,p2, q2,p3 and q3, were used to construct the feedforward lift control input through the model based predictive control algorithm. Simulations were performed to determine the lags between the activation of two solenoids according to the given reference lifts. The exhaust valve was identified earlier and used as the plant in the simulations. The measured back pressure at which the exhaust valve opens against was used to keep the configuration of the simulation consistent with that of the experiment. The results are displayed in Figure 4.19. The diagrams in the left column are the valve lift output from the exhaust valve model. Those in the right column are the calculated feedforward lift control inputs which are the calculated lags between the activation of the first and second solenoids. The lag was found to be about 3.8ms (top right), 4.1ms (middel right) and 4.8ms (bottom right) to achieve the target lift of 6mm (top left), 8mm (middle left) and 10mm (bottom left). 4.6 Conclusion A mathematical exhaust valve actuator model and an in-cylinder pressure model have been developed for a model based predictive lift control for the exhaust valve. The exhaust valve model was approximated by a partially linearized second order spring-mass-damper system. The in-cylinder pressure was modeled during the exhaust valve opening stage. This model was integrated with the exhaust valve actuator model for control development. The thermodynamics data used in this model was obtained with the WAVETM simulation which was calibrated using experimental in-cylinder pressure data. The in-cylinder pressure model was validated using experimental data and demonstrates satisfactory model accuracy. ' A model based predictive control strategy was developed for feedforward control. This strategy contains three segments; peak displacement calculation, model based initial condi- tion prediction and Kalman state estimation. Simulations were carried out which includes 110 Piecewise linearization of the pressure force at the back of the exhaust valve in 20 cycles Pressure force ( N) 0.002 0.040 ‘ Valve displacement (m) Figure 4.18. Piecewise linearization of the measured exhaust valve back pressure force 111 Calcultation of nominal Target valve lift (m) lift control input (sec) 10mm target 8mm target 6mm target Figure 4.19. Calculation of the feedforward exhaust valve lift control inputs for three set points using the measured valve back pressure 112 the white noise at the measurement side to test the performance of every individual segment and the entire feedforward algorithm assembled from these segments. A proportional and integral controller was used for closed loop control. Combined with model based predictive feedforward control, the closed loop control system for valve lift was evaluated. This was accomplished by simulations using the developed exhaust valve and in—cylinder pressure models at different reference lift points and included measurement noise. The simulation results demonstrate that the steady state valve lift error is below 0.6mm. The exhaust valve tracks the reference lift within a single engine cycle having a lift error less than 0.5mm in simulations. A real time closed-loop exhaust valve control algorithm is developed using the model based predictive control strategy. It will be evaluated by experiments in chapter 5. 113 CHAPTER 5 Experiment Implementation 5.1 Introduction In the early chapters, valve actuator system models were created and the closed-loop control strategies for both intake and exhaust valves were developed and the lift control algorithms were validated by simulations. The valve timing control depends on the reliability of the lift control and the idea of timing control are similar as that of the lift control. Therefore, chapter 5 focuses on the experimental implementation and evaluation of the developed intake and exhaust valve lift control systems. 5.2 Experiment Setup 5.2.1 Mechanical System Configuration Experiments were conducted on a 5.4L 3 valve (2 intake valves and 1 exhaust valve) V8 engine head. As displayed in Figure 5.1, the cam and cam shaft were removed from the engine head. Three electro-pneumatic actuators were installed on the top of each valve to manage the intake and exhaust valve events. Micro-EpsilonTM point range sensors were mounted under each valve to measure the valve displacements (see Figure 5.2). To test the exhaust valve control system. a pressurized chamber was installed under the 114 test poppet valves, which imitates the in-cylinder pressure acting at the back of the exhaust valve. The pressure chamber is shown in Figure 5.3. It was pressurized throughout every experiment with the supply air pressure of 65psi. The pressure inside drops immediately when the exhaust valve opens and builds up when it Closes. The exhaust lift control experiments were performed at the engine speed as low as 600RPM to ensure that the chamber pressure recovers to as high as 60psi at every cycle. An optical window was built underneath the exhaust valve on the bottom of the chamber The exhaust valve laser sensor sends and receives laser beam through this optical window to detect the exhaust valve displacement. A pressure transducer was mounted at the side wall close to the exhaust valve head. The pressure transducer provided a relative reading whose maximum value was set to be 60psi. Figure 5.1. Top view of EPVA installed on the 5.4L 3V V8 engine head 5.2.2 Control System Hardware Configuration A real time modular Opal-RTTM control system was employed as a prototype controller for the EPVA bench tests. The system consists of: 115 Figure 5.2. Point range laser valve displacement sensors Figure 5.3. Pressure chamber under the valves 116 Two 3.2GHz CPU’s An IEEE 1934 fire wire serial bus with the data transfer rate at 400MHz per bit Two 16 channel A/ D and D/ A boards with less than 1 its conversion rate One 16 channel digital I / 0 board at 50 ns sampling rate Engine Control Valve Control (Visteon) (ARES) 1 ms 40 us 16 ch 16 ch CPU#1 CPUfl 16 ch DIA AID 3.26M: $53234 3.26l-lz DIA 2 US 1 US engine 400MHZ/b valve 2 us control control throttle _, cam position position —> ignition timing solenoids mass _’ crank —> fuel control airflow angle —> injector valve manifold gate —> cam phaser displacement *—slgnal h - l id pressure _, »——> c arge motIon so eno and (syn) control cgrregt: t c am r tempera ure Def A pressure air fuel _, n n Def B ratio — coolant temperature UEGO —> Figure 5.4. Modular control system configuration 117 Figure 5.4 displays the hardware configuration of the system. CPU #1 is used for engine controls and CPU #2 is dedicated to the valve actuator (EPVA) control. An IEEE 1934 fire wire serial bus is used for communication between CPU #1 and CPU #2. CPU #1 is configured to be updated every lms and execute the engine control every combustion cycle. This means that this CPU updates input and updates analog outputs every lms, but calculates the engine control parameters every engine combustion event. The digital outputs of CPU #1 are synchronized with the engine crank angle with one-third crank degree resolution. The crank angle calculation is completed within the digital I/O card of CPU #1 utilizing digital inputs from cam sensor, gate and crank signals from an encoder. The CPU #1 digital outputs are spark pulse, fuel injection pulse, charge motion control, and intake and exhaust valve timing pulses, especially the pulses De f A and De f B that synchronize the valve control between the engine and valve control system. The inputs of the 16 channel analog I/O board include ionization signal, pressure signal, throttle position, mass air flow rate, coolant temperature, manifold pressure and temperature, and air fuel ratio from universal exhaust gas oxygen (UEGO) sensor. _The valve control CPU #2 is configured to operate at 401w sample rate, which is close to one crank angle degree at 4000RPM. CPU #2 executes most of the valve control algorithms and generates the control signals for the pneumatic valve actuators. A 16 channel A/ D board reads De f A and De f B pulse signals from CPU #1, valve lift signal from valve lift position sensors, solenoid current signals from their drive circuits, and supply air pressure signal. The solenoid control pulses and the exhaust valve pressure (which is needed to calculate the feedforward lift control inputs in simulation) are the output from a 16 channel D/ A board. A dSPACETM Autobox was utilized to run an engine simulator which provides the engine crank angle, gate signal, speed and other control parameters to both the engine controller and EPVA controller in real time application. As displayed in Figure 5.5, the black box at left and right is the Opal-RTTM control system for the valve actuation and engine control respectively. The white box sitting on the Opal-RTTM system is the dSPACETM engine simulator. 5.2.3 Valve Actuator Driving Circuit The intake valve solenoid driving circuit was designed to amplify the signal from the D / A controller outputs. Besides, it measures the solenoid current. The circuit is required to 118 Figure 5.5. Control hardware have a short solenoid release time and fast switching capability with low noise. A single channel driving circuit drawing is shown in Figure 5.6. This circuit consists of a switching MOSFET (Metal-Oxide Semiconductor Field-Effect Transistor) and a NPN BJT (Bipolar Junction Transistors). The solenoid current is measured across a 0.59 resistor in serial with the source of the MOSFET. The exhaust valve solenoid driving circuit used the peak and hold scheme to minimize the solenoid electro-magnetic delays. The total solenoid delay including the electro—magnetic and mechanical delays was kept below 2ms using this circuit. The intake and exhaust driving circuit boxes are shown in Figure 5.5 too. 5.3 Experimental Evaluation on Intake Valve Lift Control System 5.3.1 Statistical analysis of Open-loop Valve Bench Data Before the closed-loop valve lift and timing control bench tests were conducted, a statistical study focusing on the valve response repeatability was performed on test bench at both 119 E EL-solenoid D1: 2A : : 02: 24v 1w 5 ER-solenoid L .'=160hm _s = 1.20”" Mos: IRF640N Vgs(th) = 4volts Rd = 2200hm g; curreint Rss = 0.5ohm fir I feedback Ho Figure 5.6. Solenoid driving circuit 120 high and low engine speeds. The test bench uses the EPVA actuators installed on a 5.4 liter 3-valve V8 engine head. Results of this study will be used to compare with those of the closed-loop valve lift test data to evaluate the steady state closed-loop lift control performance in Closed-loop Valve Lift Control Experimental Responses session. The valve repeatability has a great impact on the adaptive estimation and steady state response. The operational conditions that were used in the open-loop parameter identification in valve lift tracking tests were the same for both the low and high engine speeds. They were applied to collect these sample data. This means that the lag between the activation of solenoids 1 and 2 is set to be a constant value 512. used in the open-loop period in the lift tracking tests. The solenoid pulse period and pulse width, the air supply pressure and the oil pressure were held constant in both types of experiments. Low engine speed open-loop valve bench data Five bench tests were conducted using 80psi air supply pressure, 90psi oil pressure, 100ms solenoid period, which corresponds to the engine speed at 1200rpm, with 25% pulse duty cycle and a lag of 5ms between the activation of two solenoids. The valve lift was targeted to be 9mm and there was a holding period on the valve lift profile under this experiment configuration (see Table 5.1). Two hundred-cycle data was collected from each experiment. The purpose of running these tests is to analyze statistical characteristics of the valve responses. Their histograms were plotted and the mean and standard deviation of responses were calculated. Taking data group #3 as an example, Figure 5.7 shows the histogram of data group #3, where the top plot is the valve lift histogram which reflects the valve lift repeatability and the bottom one is the histogram of the valve lift integral during the valve opening which indicates the repeatability of the engine charged air. For the valve lift diagram, the horizontal axis is the valve lift ranging from 8.4mm to 9.8mm and the vertical axis is the number of occurrence for each valve lift; and for the bottom diagram, the horizontal axis is the integral area and the vertical axis is the number of occurrence. The mean u and the standard deviation 0 were calculated, and the mean of integral area 121 of the valve lift was normalized to one. The 30 value was used to indicate 95% occurrence. 80psl air supply. 90psi oil pressure, 100ms solenoid period with 25% pulse width 5ms lag between the activation of two solenoids 9:: Histogram of 200 cycle data points of the open loop valve lift N p= 9.1609mm 30’: 0.85785mm g i _I Number of occurrence -5 a0"! .4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 Valve lift (mm) Histogaam of 200 cycle data points of the open loop area under the valve lift profile a I i I I I I I I 0 l1= 1 36: 10.063% IIIIIIIII JAAAA ONhOOON‘Om Number of occurren 0.195 0.2 0.205 0.21 0.215 0.22 0.225 0.23 0.235 0.24 Area under the valve lift profile (mm sec) Figure 5.7. Histogram of open-loop valve lift bench test data points for 9mm target lift at 1200rpm in 200 cycles The statistical analysis results of five data groups were summarized in Table 5.1. For the valve lift. group #5 has the largest valve lift mean at 9.55mmm and group #2 has the smallest mean at 8.83mmm. The largest 30 valve lift, 0.86mm, is from data group #3. The smallest 30 valve lift (0.44mm) was from data group #1. Regarding the analysis of the integral area of every cycle, the mean values were normalized to one. the 30 values were calculated associated to normalized data and interpreted as percentage. Among the five data group, #3 has the largest 30 value of 10.06%. Group #3 data provided the largest variation in both valve lift and the integral area. The corresponding histogram was displayed in Figure 5.7 and it will be compared with the closed-loop histogram of the 122 Table 5.1. Statistical study of open-loop valve actuation data with 9mm target lift at 1200rpm Engine configuratfon Data ymax yarea group = LL :i: 30 (mm) = n :l: 30 80psz' air supply pressure #1 9.691 :t 0.43783 1 :1: 4.639 0 90psz' oil pressure #2 8.8256 :i: 0.80343 1 :l: 10.87% 100ms valve operation period #3 9.1609 :1: 0.85785 1 d: 10.063% 25ms valve opening duration #4 9.354 i 0.5068 1 :1: 6.7673% 5ms lag of S2 (with holding) #5 9.5495 :t 0.71124 1 3: 8.0833% largest variation operated with a 9mm reference lift to show the valve lift repeatability improvement at the same operational condition due to closed-loop control. High engine speed open-loop valve bench data Similar to the low engine speed case, five bench tests were conducted using 80psz' air supply pressure, 90psz' oil pressure, 24ms solenoid period (which corresponds to the engine speed at 5000rpm) with a 25% pulse duty cycle and a lag of 5ms between the activation of two solenoids. There is no holding pattern displayed in the valve lift profile when the engine is operated at 5000rpm. In this case the valve returns before the hydraulic latch is engaged to hold the valve open (recall the discussion in the System Dynamics section). The desired valve lift was also set to be 9mm for this experiment (see Table 5.2). T wo hundred-cycle data was collected for each experiment. The mean u and the standard deviation 0 were calculated. The mean of the valve lift integral was normalized to one as well. Again, the 30 values were used to cover 95% sample data points. Table 5.2 summarizes the statistical analysis results of five data groups. For the valve lift, data group #1 has the largest mean valve lift at 9.14mm and group #5 has the smallest mean valve lift at 8.59mm. The largest 30 valve lift was from data group #4 at 0.63mm which is less than the largest 30 valve lift (0.86mm) at low engine speed (1200rpm). The smallest valve lift 30 value of 0.17mm was found from data group #2. It is less than the largest valve lift 30 value (0.44mm) from the 1200rpm tests. This indicates that the valve lift repeatability improves at high engine speed. For the integral area, data group #4 has the largest 30 value of 11.7%. The group #4 test results show the largest variation in both 123 Table 5.2. Statistical study of open-loop valve actuation data with 9mm target lift at 5000rpm Engine configuration Data ymax yarea group = [I i 30 (mm) = p :t 30 80psz' air supply pressure #1 9.1424 :1: 0.26838 1 :1: 6.1233% 90psz' oil pressure #2 9.1281 i 0.17305 1 i 4.4528% 24ms valve operation period #3 9.0284 :1: 0.39827 1 d: 8.339% 6ms valve opening duration #4 8.8649 :1: 0.6346 1 d: 11.7% 5ms lag of S2 (without holding) #5 8.5943 :1: 0.42403 1 :1: 5.545% valve lift and the integral area of the valve lift. Their histograms are shown in Figure 5.8, where the top histogram is for the valve lift and the bottom one is for the integral area. For the top diagram, the horizontal axis is the valve lift ranging from 8.9mm to 9.5mm and the vertical axis is the number of occurrence of each valve lift. For the bottom diagram, the horizontal axis is the integral area and the vertical axis is the number of occurrence of integral area. This histogram will be used to compare the corresponding closed-loop test data later. Open-loop low valve lift bench data The EPVA is capable of providing a valve lift as low as 3mm. This subsection studies statistical property at low valve lift to determine if the low valve lift operation mode is acceptable for engine control. Since the valve lift repeatability improves as engine speed increases (from the previous analysis), we are going to study the low valve lift operation only at low engine speed (1200rpm). Five bench tests were conducted using the same experimental setup as high lift case at 1200rpm engine speed except the lag between the activation of two solenoids was reduced to 3.4ms to obtain the targeted valve lift at 3mm. The statistical results were shown in Table 5.3. The mean valve lift varies from 2.68mm to 3.51mm. The largest valve lift 30 value is 2.5mm from data group #3 and the 30 value is not less than 0.8mm among the rest of the data groups. Consequently, data group #3 has a 30 integral area value as high as 73.196%. Although the actuator is capable of providing a lift as low as 3mm, its repeatability is not good enough to deliver a stable air flow when engine is operated at light load conditions. For this engine control project, the 124 80psi air supply, 90psl oil pressure, 24ms solenoid period with 25% pulse width 5ms lag between the activation of two solenoids Histogram of 200 cycle data points of the open loop valve lift w 50 0 g _. t l1= 8.8649mm ‘ 3 36: 0.6346mm: 8 - '5 . I- _. O .c - E _ 3 z 0 8.9 9 9.1 9.2 9.3 9.4 9.5 Valve lift (mm) Histogram of 200 cycle data points of the open loop area under the valve lift profile :n av lllllllll Number of occurrence 00.042 0.043 0.044 0.045 0.046 0.047 0.048 0.049 Area under the valve lift profile (mm- sec) Figure 5.8. Histogram of open-loop valve lift bench test data points for 9mm target lift at SOOOrpm in 200 cycles 125 Table 5.3. Statistical study of open-loop valve actuation data with 3mm target lift at 1200rpm Engine configuration Data ymax yarea group = ,u :l: 30 (mm) = p i 30 80psz' air supply pressure #1 2.6751 :l: 0.89005 1 :l: 15.71% 90psi oil pressure #2 3.3175 i 0.79791 1 i 18.745% 100ms valve operation period #3 3.3581 :l: 2.4954 1 :t 73.196% 25ms valve opening duration #4 3.5056 :l: 0.94671 1 2‘: 18.803% 3.4ms lag of S2 (with holding) #5 3.1683 :l: 1.432 1 :1: 41.194% valve lift operational range is to be limited between 5mm and 11mm to ensure the desired repeatability. When the required valve lift is below 5mm at light load condition, a flap valve or a throttle would be used to reduce the intake air flow. 5.3.2 Closed-loop Valve Lift Control Experimental Responses The closed-loop valve control algorithms were verified on the valve test bench utilizing the same engine head as open-loop cases. The experimental responses at both low and high engine speeds are presented in this section. Since both closed-loop valve opening and closing timing controls are similar to the valve lift control case, the results are not presented. Air and oil supply pressure for all tests are 80psz' and 90psz' respectively. The experimental parameter is 100ms solenoid period with 25ms solenoid active duration (25% duty cycle) corresponding to 1200rpm in the low engine speed tests and 24ms solenoid period with 6ms solenoid active duration (25% duty cycle) corresponding to SOOOrpm in the high engine speed tests. The initial lag between the activation of solenoids l and 2 during the open-loop parameter identification period was 5ms at both low and high speed tests. Experimental results at low engine speed 2500 cycles of valve responses were recorded with various reference valve lift points. The estimated parameter was converged in the first 25 cycles (or 2.5ms). The reference valve lift varies every 500 cycles from 9mm to 6mm, from 6mm to 10mm, from 10mm to 7mm, and from 7mm to 9mm. Their steady state responses are presented in Figures 5.11, 5.13, 126 5.15 and 5.17. On the top diagram of every figure, the black line is the reference valve lift, and the grey line is the actual valve lift. The bottom diagram shows the lift error between the reference and the actual valve lifts. They start at 50 cycles before the reference valve lift step change and end right before the next reference valve lift change. The top diagrams of Figures 5.12, 5.14, 5.16)and 5.18)display the nominal input 510 (solid line) calculated based on the estimated C f1 against the controlled input (fl (dotted line) which is the output of the PI feedback controller. Their enlarged transient responses are presented in the bottom diagrams, where the dark lines are the reference valve lift and the grey lines are the true valve displacement. Open-loop parameter identification valve responses Figure 5.9 enlarges the first 80 cycle valve lift tracking responses. C f1 identification error (the bottom diagram) converges to a set tolerance in about 25 cycles. It can be observed from the top diagram that the system switched from the open-loop to closed-loop control at the 65th cycle where the lift error jumps from zero to 0.7mm (the dark grey line in the top diagram). This indicates that the closed-loop controller is engaged. Steady state responses of valve lift tracking During the steady state operations, the valve lift tracks the reference valve lift and oscillates around the reference values. The responses show good repeatability at high valve lifts. The maximum absolute valve lift error was bounded by 0.4mm at 10mm lift and 0.5mm at 9mm lift. The repeatability is relatively lower at low lift, however, the valve lift error falls mostly in the region of :l:0.5mm at 6mm and 7mm lift. This is partially due to the fact that the pneumatic valve actuator has a higher sensitivity at the low valve lift, which results in a high steady state lift error. The maximum absolute steady state error at these four set points are listed in Table 5.4. The statistical performance of the valve lift responses with the closed-loop controller is also important to study. The statistical characteristics of the open—loop valve lift are 127 Valve3lift in open loop parameter identification period Io: 19' - . . E :agtaia'mi 2 _ —lI error _ -2 - J I 1 I I l l Cf1 estimation in open loop parameter identification period lift and error (m) 6! I l l _L N O f .. a -l l O Cf1 (mlsec) #m 0 Lift errof in Cf1l|D window in I x 110-3 openloop parameter identification period NO error (m) |II|I|IIII III I I II III I l Th .- 10 20 30 40 50 60 70 80 number of cycles I'o Figure 5.9. Open-loop parameter Cf1 identification at 1200rpm Table 5.4. Maximum SS absolute valve lift error ( 1200rpm) I Reference valve Hts (mm) II 6 I 7 I 9 I 10 I I Max. absolute lIft error (mm) II 0.75 I 1.3 I 0.5 I 0.4 I 128 Table 5.5. Statistical study of closed—loo valve actuation data at 1200rpm Engine configuration Data gm” yarm group = It i: 30 (mm) = p :t 30 80psi air supply pressure #1 9.2358 :l: 0.454 1 :l: 5.4534% 90psz' oil pressure #2 9.2495 i 0.3478 1 :b 2.9224% 100ms valve operation period #3 9.0984 :l: 0.38628 1 i 4.8195% 25ms valve opening duration #4 9.0549 :1: 0.44419 1 :t 5.1670% 9mm reference valve lift #5 9.1015 :t 0.41092 1 a: 4.1833% (with holding) analyzed in the earlier section of Statistical Analysis of Open-Loop Valve Bench Data. The results of the valve lift statistical study shown in both Figure 5.7)and Table 5.1 provide the worst lift 30 value at 0.86mm and the worst integral area 30 value at 10.87% with the valve lift at 9mm using five test data groups. The same statistical analysis is conducted for the closed-loop lift control. Five 200 cycle steady state valve lift responses at 9mm were used to calculate the means and standard deviations of the valve lift and its integrated area. These results are compared with the open—loop results. The diagrams displayed in Figure 5.10 depict the histograms of the lift and integral area of the valve lift profile. They are obtained from the data group with the largest variations among all five data groups (see group #1 in Table 5.5). Note that the axes ranges and the bin width of the valve lift (top) and integral area (bottom) histograms in Figure 5.10 are the same as those in Figure 5.7 for an easy comparison. The five sets of means and 30 values of valve lift and integral area were summarized in Table 5.5. The worst 30 value of the valve lift reduced from the open-loop 0.86mm to the closed loop 0.45mm, and the worst integral area 30 value reduced from 10.87% to 5.45% (see both Table 5.5 and Table 5.1). In other words, the worst case 30 values of both valve lift and integral area were reduced by about 45%. This indicates that the closed-loop valve lift control reduces the valve lift variation, and hence, improves its lift repeatability. Transient responses of valve lift tracking The feedforward nominal input 510 remains steady due to the fact that the parameter identification convergence is preserved in the closed-loop lift control operation. It takes 129 80psi air supply, 90psi oil pressure, 100ms solenoid period with 25% pulse width Closed-loop valve lift control with 9mm referecen lift Histogram of 200 cycle data points 60 The valve lift data at steady state 50- ........ 1 ........ . ........ 40.. 30-. 20 p. 10* 08.48.6 Number of occurrence . 9 9. 2 9.. Valve lift (mm) The area under the lift profile at steady state 60 _ I 501-1 , . ...... ...; ..... . ..... .. 40» ' '1 30p 20»- m»~ 0 0.195 0.2 0.205 0.21 0.215 0.22 0.225 0.23 0f235 0.24 Area under the valve lift profile (mm. sec) Number of occurrence Figure 5.10. Histogram of closed-loop valve lift control test data points for 9mm reference lift at 1200rpm in 200 cycles 130 about one cycle for the valve to reach the reference valve lift with less than 0.5mm of lift error. This is critical for transient air charge control. The controlled input (fl is close to the nominal input 510 which is sufficiently accurate to bring the valve lift close to the reference valve lift in the first cycle. In all four cases, the actual valve lift is within 0.5mm lift error region of the reference lift in one cycle. x 10'3 Reference valve lift vs. actual valve lift '2‘ v —reference lift g —actual lift 0 Z I! > 450 500 550 600 650 700 750 800 850 900 950 1000 x 10'3 Valve Ilft error E § I- 0 E 0 2 G > 450 500 550 600 650 700 750 300 850 900 950 1000 number of cycles Figure 5.11. Steady state valve lift tracking responses from 9mm to 6mm lift at 1200rpm 5.3.3 Experimental Results at High Engine Speed The high speed closed-loop valve lift tracking results are presented and discussed in this subsection. Similar to the low speed case, 2500 cycles of valve responses were collected with multiple reference valve lift set points the same as these in the low engine speed case. The entire 2500 cycle lift tracking responses and two enlarged transient responses are shown in 131 x 10 -3 810 and 51 6 I I I I I a w I 8 5.5 b | -_ I —810 - 3.”; 5 A _ .33 ' " 51 u 4.5 _ _ ' - 5 4 - ---- *-- ‘3'- 9‘-'au"a"al‘10'l'.'"'.'t'm‘ 0 (go 3.5 r ‘ 3 450 500 550 600 650 700 750 800 850 900 950 1000 x 10 '3 Transient response of valve lift tracking 1o ,_ I I I I .4 ’E‘ 9.5 , _ , - . ~ v 895 : —reference lift : :13 8 _ —actual lift _ 5 7i5 f l 9 6.5 — - 6 _ 555 - ~ 500 501 502 503 504 505 507 508 number of cycles Figure 5.12. Controlled input and transient valve lift tracking responses from 9mm to 6mm lift at 1200rpm 132 11x 10 Reference valve lift vs. actual valve lift valve lift (m) —reference lift _ —actual lift . I I I I I I I T I I 10- ' q .1 .4 Ere 50 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 .3 x 10 Valve Ilft error I I j I I I I valve ift error (m) .a 0 d N w ¥ 0| l l l .950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 number of cycles Figure 5.13. Steady state valve lift tracking responses from 6mm to 10mm lift at 1200rpm 133 6 x 10 310 and 31 A 5. I ___r__r___r__|_~_ ‘ _____ ' _. 3. 5 ' - «I; 4. —810 I s -- 31 fl 4 a .9 3. , <00 3 I I 1 1 l l 1 1 l 1 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 11 x 10.3 Transient response of valve lift tracking ———\—fi 3 10— I F :c: ,- ~ - — 8 —reference lift . 3 ” —actualllft g 7 - . 6 =‘1.—__i ‘ 5 1 I 1 I 1 1 1 1000 1001 1002 1003 1004 1005 1006 1007 1008 number of cycles Figure 5.14. Controlled input and transient valve lift tracking responses from 6mm to 10mm lift at 1200rpm 134 b x 10 Reference valve lift vs. actual valve lift 11 I I T I I I I I I l E 10* ~ .. —referenceliftd 5 9 —actual lift 2 ° ’ _ * To 7 - . > e . I“ - 5 .- 1 l l l l I l 1 1 L l - 1450 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000 x 10'3 Valve lift error E 3 t o E 0 z ‘s' 2 61450 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000 number of cycles Figure 5.15. Steady state valve lift tracking responses from 10mm to 7mm lift at 1200rpm 135 810 and 31 (890) A 3 1 l 1 1 1 1 1 1 1 1 1450 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000 x 10 -3 Transient response of valve lift tracking 11 a a , , , , . 10':—1 - - . . , 7 , _ E 9 ’ ~ —reference lift _ V —actual lift 5 s — . . w . , - I s 7* ‘ __ g 5 ‘ . . 5 . . .1 . 1500 1501 1502 1503 1504 1505 1506 1507 1508 number of cycles Figure 5.16. Controlled input and transient valve lift tracking responses from 10mm to 7mm lift at 1200rpm 136 E 9 3 L g 8 —reference lift 1 E 7 —actual lift a 6 r . 5 1 1 I I I 1 1 1 1 I 1950 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 3 x 10'3 Valve llft error E 2.5 »- « I- 2 g 1.5 C 1 I E g 0.5 7,, 0 _ > -0. . .1950 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 numberofcycles Figure 5.17. Steady state valve lift tracking responses from 7mm to 9mm lift at 1200rpm 137 S10 and 81 A o -1 0 a a 1 r «n 3]-: .1 L L (0‘6 - u‘- a" - ' s . ~ u —610 d A 3 -- 81 <00 ~ 4 3 l 1 1 1 1 1 1 I 1 1 1950 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500 11 x 10‘3 Transient response of valve lift tracking A 10— q .5. E 9 p ‘-———\I_____, a a L . . is 7 . —reference lift _ > —actual lift 6 I a 5 2000 2001 2002 2003 2004 2005 2006 2007 2008 number of cycles Figure 5.18. Controlled input and transient valve lift tracking responses from 7mm to 9mm lift at 1200rpm 138 Figure 5.19. The top diagram displays the reference valve lift in black line, the actual valve lift in light grey and the lift error in dark grey; the middle diagram shows the transient response at the reference lift change from 10mm to 6mm, and the bottom diagram shows the transient response at the reference lift change from 7mm to 9mm. All the horizontal axes are the number of engine cycles. The vertical axes are the valve lifts in m. The estimated parameter was converged within 100 cycles (or 2.4ms) which was indicated by a small jump on the reference valve lift on the top diagram. In most of cases, it takes about one cycle for the valve to reach the reference valve lift with less than 0.5mm of lift error. However, when the reference lift has a relatively large drop, the actual lift would have a big undershoot during the transient response (see the transient response from 10mm to 7mm in the top diagram of Figure 5.19). The undershoot is about 1.9mm in this case for the first step, and 0.5mm after the first step. This is partially due to the supply air pressure variations of different lift conditions at high engine speed. The high air flow requirement at high valve lift operational conditions reduces the actual supply air pressure close to the actuator, and supply air pressure increases as the valve lift reduces. When the valve is transient from high lift to low lift, the supply air pressure increases gradually, causing larger undershoot since the feedforward control assumes higher supply air pressure than actual one. This problem can be resolved by increasing the volume of the planum at the supply air manifold of the actuator cylinder. The maximum absolute steady state error at these four set points are listed in Table 5.6. The steady state lift errors are less than 0.8mm at high valve lift and less than 1.1mm at low lift. The results of the valve lift statistical study at 5000rpm engine speed shown in Table 5.6. Maximum SS absolute valve lift error ( 5000rpm) Reference valve lifts (mm) 6 7 9 10 Max. absolute lift error (mm) 0.8 1.1 0.8 0.7 both Figure 5.8 and Table 5.2 provide the worst lift 30 value at 0.63mm and the worst integral area 30 value at 11.7% with the target lift at 9mm using five test data groups. 139 valve lift Figure 5.19. Valve lift tracking responses with multiple reference lift at 5000rpm and error (In) valve lift (m) valve lift (m) x 10 Reference valve lift vs. actual valve lift 12 - ¥ , 5 ~ - < ‘—rreference lift 3 ...aauanmi 7 ., ":lifterror, 0 3 500 1000 1500 2000 2500 x 10 Transient response of valve lift tracking from 10mm to 6mm 1°F_, , . w x .] —referencelift: 8 + \ .. ~ ~ . —actual lift . 4500 ‘3' 5'01 ‘ 5'02 503 l 504 1 505 11 x 10 Transient response of valve lift trackLngr from 7mm to 9mm _ .................. , . , ,- 9 r '* ‘ ‘ . 7 *' ‘ I l """""" ‘ —*‘.refere'n¢e lift ‘ _ . eactuallift, I 52000 2001 2002 2003 i 2004 2005 number of cycles 140 Table 5.7. Statistical study of closed—loop valve actuation data at 5000rpm Engine configuration Data gm“ yarea group =pi30Imm) =p:t30‘ 80psz' air supply pressure #1 9.0439 i 0.45208 1 :t 9.4497 (0 90psi oil pressure #2 9.0832 :1: 0.28338 1 i 5.1215% 100ms valve operation period #3 9.1641 :i: 0.313 1 2}: 7.4794% 25ms valve opening duration #4 8.9544 :1: 0.24869 1 :i: 6.69% 9mm reference valve lift #5 9.091 :t 0.37342 1 :1: 8.268270 (without holding) The same statistical analysis is performed for the closed-loop lift control. Five 200 cycle steady state valve responses at 9mm reference lift were used to calculate the means and stande deviations of the valve lift and its integral area. These results are compared with the open-loop results. The diagrams displayed in Figure 5.20 depict the histograms of the valve lift and integral area with the largest. variations (data group #1 in Table 5.7). For easy comparison, the axes ranges and the bin width of the valve lift (top) and integral area (bottom) histograms in Figure 5.20 are the same as those in Figure 5.8. The five sets of means and 30 values of valve lift and integral area were summarized in Table 5.7. The worst 30 value of the valve lift reduced from the open-loop 0.63mm to the closed-loop 0.45mm which was reduced by about 29%. The worst integral area 30 value reduced from 11.7% to 9.45% which was reduced by about 19% (see both Table 5.7 and Table 5.2). The low engine speed closed-loop lift control data showed a reduction of about 45% on both the 30 values of the valve lift and integral area in their worst case. The reduction on the cycle to cycle lift variation at 5000rpm seems lower than that at 1200rpm. We believe that low improvement at high engine speed is mainly due to the fixed control sample rate which reduces the valve control resolution as engine speed increases. 5.3.4 Concluding Remarks On Intake Valve Lift Control System In chapter 2. A nonlinear mathematical model called the level one model was developed for the electro-pneumatic valve actuator based on Newton’s law, mass conservation and thermodynamic principles. A control oriented model, called level two model, was estab- lished using the physics based nonlinear model for model reference parameter identification 141 80psi air supply, 90psi oil pressure, 24ms solenoid period with 25% pulse width Closed-loop valve lift control with 9mm referecen lift Histogram of 200 cycle data points The valve lift data at steady state fii ‘r Number of r .3 O 8.4 8.8 9 Valve lift (mm) 100 The area under the lift profile at steady state C 60 Z g6: 3.449770 : Number of 0.038 0.04 0.042 0.044 0.046 0.048 Area under the valve lift profile (mm-sec) Figure 5.20. Histogram of closed-loop valve lift control test data points for 9mm reference lift at 5000rpm in 200 cycles 142 in chapter 3. This level two model reduces computational throughput and enables real time implementation. A model reference adaptive scheme was employed to identify two key nonlinear system parameters. The identified parameters are then used to construct the feedforward control as part of the closed-loop valve PI controller. The closed-loop valve lift tracking, and valve opening and closing timing control strategies were developed. In chapter 5, the lift control algorithm was validated on an electro-pneumatic valve actua- tor test bench. The test data covers multiple reference lift points at both 1200rpm and 5000rpm engine speeds for both steady state and transient operations. The experiment results showed that the actual valve lift reached the reference lift within 0.5mm of lift error in one cycle at 1200rpm and in two cycles at 5000rpm. The maximum steady state lift errors are less than 0.4mm at high valve lift and less than 1.3mm at low valve lift. Furthermore, the closed-loop valve lift control improved valve lift repeatability with more than 30% reduction of standard deviation over the open-loop control. 5.4 Experimental Evaluation on Exhaust Valve Lift Control System 5.4.1 Experimental Results of Closed-Loop Exhaust Valve Lift Tracking Finally, Figure 5.21 to 5.24 present the closed-loop lift tracking experimental results with the feedforward control. The purpose of the experiments were to evaluate the system feedforward input calculation. The PI gains were kept relatively low in the experiments to allow the feedforward response to be dominant. 150 cycles of valve responses were recorded with sequences assembled at three reference lift set points in Figure 5.21. The reference valve lift varies every 50 cycles from 8mm to 6mm, 6mm to 10mm, and 10mm to 8mm. The complete sequences of lift tracking responses are presented in Figures (5.21). The responses at every set point were enlarged through Figure 5.22 to 5.24 to illustrate their 143 transient and steady state performance. On the top diagram of every figure, the black line is the reference valve lift, and the grey line is the actual valve lift. The bottom diagram shows the lift error between the reference and the actual valve lifts. Figure 5.22 shows that the exhaust valve follows the reference lift of 6mm in two engine cycles with the lift error less than 0.7mm. Figure 5.23 and 5.24 show that the exhaust valve tracks the reference lift of 10mm and 8mm. in one engine cycle with the lift error less than 0.7mm. The enlarged responses display that the absolute steady state lift tracking error of all three set points is below 1mm. Here, an accurate feedforward controlled input ensures a fast transient repones. The valve responses at low lift is more sensitive to the error in the calculated feedforward controlled input, which has relatively greater fraction in the entire input (the lag between the activation of solenoid #1 and #2). A slight error in the feedforward input calculation due to the model uncertainty, measurement inaccuracy or numerical error leads to a significant deviation of the actual valve lift from its desired lift in transition. Therefore, the valve at low reference lift exhibits a slower transient response than that at high reference lift. 5.4.2 Concluding Remarks On Exhaust Valve Lift Control Sys- tem A mathematical exhaust valve actuator model and an iii-cylinder pressure model have been developed for a model based predictive lift control for the exhaust valve. The exhaust valve model was approximated by a partially linearized second order spring-mass-damper system. The iii-cylinder pressure was modeled during the exhaust valve opening stage. This model was integrated with the exhaust valve actuator model for control development. The thermodynamics data used in this model was obtained with the WAVETM simulation which was calibrated using experimental iii-cylinder pressure data. The in-cylinder pressure model was validated using experimental data and demonstrates satisfactory model accuracy. A model based predictive control strategy was developed for feedforward control. This 144 Exhaust valve lift tracking against 60psi back pressure with cycle to cycle variation at 600RPM x10-3 # f ' — measured 10 — reference , 5m lift (m) lift error (m) 5L .. . "i 50 "is 100 {25 150 175 200 cycle Figure 5.21. Experimental results of closed-loop exhaust valve lift tracking control system with three set points 145 Exgiaust valve lift tracking from 8mm to 6mm x 10' . — measured A 9 r — referenence ‘ E a _ E 7 - 6 - 5 5 lift error (m) Figure 5.22. Enlarged experimental results of closed-loop exhaust valve lift tracking from set point of 8mm to 6mm 146 Exhaust valve lift tracking 6mm to 8mm , —— measured , . . ._ referenence lift error (m) 100 105 110 115 120 125 cycle Figure 5.23. Enlarged experimental results of closed-loop exhaust valve lift tracking from set point of 6mm to 10mm 147 Exhaust valve lift tracking 10mm to 6mm x10'3 12 . . —— measured A 10 ~ — reference . ii 93 lift error (m) $0 $2 $4 36 $3 40 cycle Figure 5.24. Enlarged experimental results of closed-loop exhaust valve lift tracking from set. point of 10mm to 8mm 148 strategy contains three segments; peak displacement calculation, model based initial condi- tion prediction and Kalman state estimation. To reduce real time computational through- put, simulations were carried out to calculate the feedforward lift control inputs through the developed model based predictive control strategy for given reference lifts. In real time application, the acquired feedforward input combined with the feed back lift compensation generated from a proportional and integral controller forms the closed-loop lift control sig- nal to accomplish the exhaust valve lift tracking. The exhaust valve model was identified and the measured exhaust valve back pressure was piecewisely linearized to obtain param- eters required for the feedforward input calculation. Both of them were employed in the simulation. Experiments were conducted on a 5.4L 3 valve V8 engine head at 600RPM engine speed to evaluate the closed-loop lift control system. A pressurized chamber was installed under the test poppet valves, which imitates the in-cylinder pressure acting at the back of the exhaust valve. The experimental results containing three lift set points demonstrated that the steady state valve lift error is below 1mm. 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