MODELING AND CONTROL OF A GASOLIN E DIRECT INJECTION F UEL SYSTEM B y Mengyan Gu A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Mechanical Engineering Master of Science 2015 ABSTRACT MODELING AND CONTROL OF A GASOLIN E DIRECT INJECTION F UEL SYSTEM By Menyan Gu Fuel economy and emissions are the two main concern s to many automobile engineers. The Gasoline Direct I njection (GDI) fuel systems are widely used in internal combustion engines to improve fuel economy with reduced emission s . This study focuses on the develop ment of a MotoTron based fuel rail pressure control system. This work is motivated by the need for maintaining higher fuel rail pressure for improved fuel injection accuracy . The developed fuel rail control system consists of a MotoTron control module , a customized actuator drive box, and a host computer with LabVIEW GUI ( graphic user interface) and the Moto T une calibration tool for MotoTron . T he Moto T ron and t he host computer communicate through CAN (control area network). A mathematical model of the fuel rail control system was developed using MATLAB / Simulink. The pressure controller for the fuel system contains three parts: a b umpless and a nti - windup PI (proportional and integral) c ontroller , a feed - forward controller , and a dead - zone compensat or . The closed - loop control was simulated and validated in Simulink using the developed model, where t he fuel injection process was also considered. T he simulation results of tracking the desired pressure were compared with the experiment data. The comparison with the Simulink simulation results and experiment data shows that the Simulink model is able to reflect the characteristics of the actual fuel rail system ; and t he experiment data show that the closed - loop controller is able to maintain the fuel system pressure at the desired level . iii ACKNOWLEDGEMENTS I would like to take this opportunity to express my sincere appreciation to many individuals who have so graciously helped me during my MS study . I would like to thank Dr. Guoming ( George ) Zhu for being my advisor and supporting me during my MS program and Dr. Harold Schock and Dr. Jongeun Choi for serving as advisors i n my MS co mmittee . An d I would also like to thank Tom Stuecken and Kevin Moran for help ing me set up the test bench and conducting the experiments . I would also like to thank students in our research group : Jie Yang, Tao Zeng, Yifan Men , Ruitao Song , and Ali M. H. Alhajjar who hel ped me to complete th e MS research project . that makes me full of courage to strive for the future. iv TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ........................ vi LIST OF FIGURES ................................ ................................ ................................ ..................... vii KEY TO SYMBOLS AND ABBREVIATIONS ................................ ................................ .......... ix CHAPTER 1: INTRODUCTION ................................ ................................ ................................ ... 1 1. 1 Motivation ................................ ................................ ................................ ................................ .. 1 1.2 Existing Work ................................ ................................ ................................ ............................ 2 1.3 Gasoline Direct Injection Fuel System Overview ................................ ................................ ..... 3 1. 3.1 System Block Diagram ................................ ................................ ............................... 3 1.3.2 Control Block Diagram ................................ ................................ ............................... 4 1.3.3 MSU System Hardware ................................ ................................ .............................. 5 CHAPTER 2: FUEL RAIL SYSTEM DEV ELOPMENT ................................ ............................... 8 2.1 Introduction ................................ ................................ ................................ ................................ 8 2.2 Experiment Equipment ................................ ................................ ................................ ............ 10 2.2.1 Sensor and Actuator Signal Processing ................................ ................................ .... 10 2.2. 2 MotoTune ................................ ................................ ................................ .................. 1 2 2.2. 3 CAN C ommunication ................................ ................................ ............................... 1 4 2.2. 4 LabVIEW GUI Development ................................ ................................ ................... 1 5 2.3 Fuel Rail System Modeling ................................ ................................ ................................ ..... 1 7 2.3.1 High Pressure Pump Model ................................ ................................ ...................... 1 7 2.3 .2 The Fuel Rail ................................ ................................ ................................ ............. 20 2.3.3 Fuel injector and Leak ................................ ................................ .............................. 2 1 2.3.3 .1 Fuel I njector ................................ ................................ ........................ 2 1 2.3.3 .2 Leak age ................................ ................................ ............................... 2 2 2.4 Fuel Pump Control ................................ ................................ ................................ ................... 2 3 2.4.1 Control Principle ................................ ................................ ................................ ....... 2 3 2.4. 2 Open - Loop Control ................................ ................................ ................................ ... 2 7 2.4. 3 Close d - Loop Control ................................ ................................ ............................... 2 7 2.4. 3 . 1 PI Controller ................................ ................................ ........................ 2 8 2.4 . 3 . 2 Dead - z one Compensation ................................ ................................ ... 2 9 2.4. 4 Feed - f orward Control ................................ ................................ ................................ 30 CHAPTER 3: SIMULATION VALIDATION ................................ ................................ ............. 3 3 3.1 Introduction ................................ ................................ ................................ .............................. 3 3 3. 2 Model Validation ................................ ................................ ................................ ..................... 3 3 3. 2.1 Tracking Validation ................................ ................................ ............... 3 6 3. 2.2 Fuel Inject Flow Compensation ................................ ............................. 3 8 v CHAPTER 4: EXPERIMENTAL VALIDATION ................................ ................................ ........ 40 4. 1 Introduction ................................ ................................ ................................ .............................. 40 4. 2 Tracking Validation ................................ ................................ ................................ ................. 40 4.3 Leak age Protection ................................ ................................ ................................ ................... 4 1 CHAPTER 5: CONCLUSIONS AND FUTU RE WORK ................................ ............................. 4 3 5.1 Conclusions ................................ ................................ ................................ .............................. 4 3 5.2 Future Recommendations ................................ ................................ ................................ ........ 4 3 APPENDI CES ................................ ................................ ................................ ............................... 4 5 A PPENDIX A - Fuel Pump Harness ................................ ................................ .............................. 4 6 A PPENDIX B - Moto T ron Simulink Diagram ................................ ................................ .............. 4 7 REFERENCES ................................ ................................ ................................ .............................. 4 8 vi LIST OF TABLES Table 1: Output Control S ignal D efinition . ................................ ................................ ................... 10 Table 2: Input Control Signal D efinition . ................................ ................................ ...................... 10 Table 3 : The Technical Features of the I njector ................................ ................................ ............ 2 2 Table 4 : Injection S ignals . ................................ ................................ ................................ ............. 2 2 Table 5 : Lookup Table for Feed - forward C ontrol ................................ ................................ ......... 3 1 Table 6: The P arameters in GDI Fuel Rail System Simulink M odel . ................................ ........... 3 4 vii LIST OF FIGURES Figure 1: PFI E ngine and GDI E ngine ................................ ................................ ............................. 1 Figure 2: Fuel Rail System Block D iagram . ................................ ................................ .................... 3 Figure 3: Fuel Rail System Control Block D iagram . ................................ ................................ ....... 4 Figure 4: Control Block I nside the MotoTron . ................................ ................................ ................ 5 Figure 5: High Pressure Fuel P ump by Pierburg Instruments Inc. . ................................ ............... 5 Figure 6: High P ressure Fuel P ump for 250 bar . ................................ ................................ ............. 6 Figure 7: Fuel Rail Pressure Control S ystem . ................................ ................................ .................. 7 Figure 8 : Fuel Rail Pressure C ontrol System D iagram . ................................ ................................ ... 8 Figure 9 : Druck PTX 7200 Series Industrial P ressure T ransmitter . ................................ .............. 1 1 Figure 10 : Supply Pressure S en sor Wire D iagram . ................................ ................................ ....... 1 1 Figure 1 1 : Chrysler Fuel S ensor ................................ ................................ ................................ ... 1 1 Figure 1 2 : High Pressure Sensor Wire D iagram ................................ ................................ ............ 1 2 Figure 1 3 : MotoTune Interface ................................ ................................ ................................ ...... 1 3 Figure 1 4 : CAN C omunication .. ................................ ................................ ................................ .... 1 4 Figure 1 5 : LabVIEW GUI ................................ ................................ ................................ ............ 1 6 Figure 1 6 : Cam D imension . ................................ ................................ ................................ ........... 1 7 Figure 1 7 : Piston D isplacement ................................ ................................ ................................ ..... 1 8 Figure 1 8 : BOSCH H igh - pressure Piezo I njector HDEV4 ................................ ............................ 2 1 Figure 1 9 : Relationship b etween the Leakage and the P ressure .. ................................ .................. 2 3 Figure 20 : Control Principle of the H igh Pressure Fuel P ump ................................ ...................... 2 4 Figure 2 1 : Pulse Signal for Solenoid Control Valve Synchronized with Crank P osition P ulse . ... 2 5 Figure 2 2 : Pulse Signal for Solenoid Control Valve before C alibration ................................ ....... 2 6 viii Figure 2 3 : Pulse S ignal for Solenoid Control V alve after C alibration ................................ .......... 2 6 Figure 2 4 : Open - loop Control S ystem .. ................................ ................................ ......................... 2 7 Figure 2 5 : Close d - loop Control S ystem ................................ ................................ ........................ 2 7 Figure 2 6 : Bumpless and Anti - windup PI C ontroller . ................................ ................................ ... 2 8 Figure 2 7 : Dead - zone D efinition .. ................................ ................................ ................................ . 2 9 Figure 2 8 : Experiment D ata of t he P ressure P erformance of S ystem w ithout F eed - forward C ontrol with I njection ................................ ................................ ................................ .. 3 0 Figure 2 9 : Volume Change due to Piston M otion from 0 to 1.2ms . ................................ .............. 31 Figure 30 : Fuel R ail System Simulink M odel .. ................................ ................................ ............. 3 4 Figure 3 1 : The Block Diagram of the C lose d - loop F uel Rail System with C ontroller ................. 3 5 Figure 3 2 : Relationship among Each S ignal . ................................ ................................ ................. 3 6 Figure 3 3 : Simulation R esult wi th the Desired P ressure of 200bar .. ................................ ............. 3 7 Figure 3 4 : Simulation Result with the Desired P ressure of 250bar ................................ ............... 3 7 Figure 3 5 : Injection without Feed - forward C ontroller at 200bar . ................................ ................. 3 9 Figure 3 6 : The Pressure Performance of the System with Feed - forward Control with I njection at 200bar .. ................................ ................................ ................................ ........................ 3 9 Figure 3 7 : The P ressure P erformance of the S ystem with F eed - forward C ontrol with I njection at 250bar ................................ ................................ ................................ .......................... 3 8 Figure 3 8 : Comparison of the E xperiment R esult and Simulink R esult at 200bar . ....................... 40 Figure 3 9 : Comparison of the E xperiment R esult and Simulink R esult at 250bar . ....................... 4 1 Figure 40 : Leak Protection at the Desired Pressure at 250bar . ................................ ...................... 4 2 Figure 4 1 : Fuel Pump Harness . ................................ ................................ ................................ ...... 46 Figure 42 : MotoTron Simulink Diagram . ................................ ................................ ...................... 47 ix KEY TO SYMBOLS AND ABBREVIATIONS Angle C os Cosine Kg Kilogram mm Millimeter mA Milliampere Density ( kg/m 3 ) A Section (m 3 ) h Piston displacement (m) K f Bulk modulus of elasticity P Pressure (bar) q Fuel flow (m 3 /s) u Control signal R Resistance ( ) U Voltage (V) BDC Bottom dead center CAN Controller area network ECU Engine control unit ECM Electronic control module GDI Gasoline direct injection GUI Graphic user interface MRAC Model reference adaptive control MSU Michigan State University x PFI Port Fuel Injection PI P roportional and integral RPM Rotations per minute TDC Top dead center 1 CHAPTER 1: INTRODUCTION 1.1 Motivation As an important key technology for improv ing the fuel economy of gasoline engines with reduced emissions , Gasoline Direct I njection ( GDI ) engine s attract a lot of attentions . Compared with traditional Port Fuel Injection (PFI) engine s , shown in F igure 1 , GDI engine s i mprove combustion efficiency with higher power density . Figure 1 : PFI Engine and GDI Engine Improved fuel economy is mainly achieved by reduc ing throttling and heat losses during stratified combustion as well as operating the GDI engines with higher compression ratios than PFI engines . Furthermore, with the GDI concept , PFI wall - wetting and carbon buildup are eliminated inside the intake ports [ 1]. For the GDI fuel system, t he gasoline is highly pressurized in the common fuel rail and injected via a GDI fuel injector directly into the individual combustion chamber . By inject ing fuel directly into the combustion chamber , the charge mixing process during the intake stroke can be precis ely control led and optimize d [2] . The fuel pressure for the fuel rail has fairly high pressure for GDI engines , and the fuel rail pressure fluctuations could aff ect fuel injection quantity accuracy and degrad e the engine performance and even damage the engine. Therefore, the GDI engine fuel rail system needs to be precisely control led , which is one of the key challenges for the gasoline direct injection technology . The main p urpose of the fuel rail control is to maintain the desired fuel rail pressure 2 under all engine operational conditions, including fuel injection events , and make the pressure fluctuations as small as possible. In this thesis, a GDI fuel rail pressu re control system was developed using PI (proportional and integral ) control and feed - forward control to minimize the fuel pressure fluctuat ion . 1. 2 Existing Work A number of studies have been conducted for the modeling and control of fuel rail systems and most of these studies are targeted at diesel engines. For example, t he fuel rail system in reference [ 3 ] is developed based on the energy conservation principle ; a physic s - based mathematic al model of the common rail system is developed in r eference [4] ; and a detailed fuel injection system simulation model for diesel engines is presented in reference [5] . Although the common fuel rail system for a diesel engine has a similar structure to the GDI fuel system, the fuel pump and the injector are quite differen t due to quite different fuel injection pressure . Therefore , model ing and control of the GDI fuel rail system is very different from the diesel fuel system . From a control point of view, back - stepping control strategy is used for the fuel rail system of a GDI engine in r eference [6] and the Model Reference Adaptive Control (MRAC) algorithm is used to reduce the residual pressure in the fuel rail in r eference [ 7 ]. This thesis intends to develop a control - oriented fuel rail model and validate it using the experiment data , and the developed model will be used for developing and validating the associated control algorithm . 3 1.3 Gasoline Direct Injection Fuel System Overview 1.3.1 System Block Diagram In this research , the fuel rail system includes a fuel tank with a low pressure pump, a high fuel pressure pump driven by a n electrical motor , a fuel rail, an injector, and a pressure relief valve. The GDI fuel rail system is able to pressur ize the fuel rail up to 250 bar . The fuel rail pressure is independent of the engine speed ; see Figure 2 for t he sy stem block diagram . Figure 2 : Fuel Rail System Block Diagram T he low pressure pump in the fuel tank increases the supply pressure to about 30 psi ( about 2 bar). The fuel flows through the pump solenoid control valve into the high pressure chamber . The solenoid control valve is controlled by a n on - off signal genera ted by the MotoTron controller and synchronized with the motor position . The GDI high pressure pump is able to raise 4 the fuel pressure up to 250 bar. The fuel rail is a small aluminum alloy container. T he injector is connect ed to the fuel rail through a fuel line . T he pressure relief valve protects the whole system from damag e due to excessive high pressure. 1.3. 2 Control Block Diagram In this thesis, a fuel rail pressure control system using a MotoTron co ntrol module i s developed. In this study , the fuel rail control system consists of a MotoTron control module , a customized solenoid drive box , and a Moto T ron control module host computer installed with MotoTune and LabVIEW . The Mo toTron and the host computer communicate through the first CAN (control ler area network) channel for real - time display and calibration . The LabVIEW GUI running on the host computer communicates with the MotoTron through the second CAN channel . Figure 3 shows the fuel rail pressure control system architecture. Figure 3 : Fuel Rail System Control Block Diagram The fuel rail pressure control algorithm i s developed in Simulink using a MotoHawk development environment that is capable of auto - cod ing, compiling, and real - time calibration. With the help of the MotoHawk development environment, the fuel pressure control algorithm can be developed efficiently , coded automatically from M ATLAB /Simulink to C , and compiled in to the MotoTron production controller [ 8 ]. T he control block diagram inside the Moto T ron control module is shown in F igure 4 . It includes the PI controller, dead - zone compensation , and feed - forward control. Each function 5 block in this control system is described in detail later . In addition, the control algorithm is also discussed in detail with simulation and experimental results. Figure 4 : Control Block inside the Moto T ron 1 . 3 . 3 MSU System Hardware The high pressure fuel pum p currently used in the MSU Energy and Automotive Research L ab i s a fuel cart produced by Pierburg Instruments Inc. as shown in F igure 5 . Figure 5 : High Pressure Fuel Pump by Pierburg Instruments Inc . 6 The Pierburg fuel cart is able to provide the fuel rail pressure to 200 bar. To have an improved charge mixing , the required fuel rail pressure could exceed 200 bar and a new fu el rail system , shown in F igure 6 , i s developed to pr ovide a fuel rail pressure up t o 250 bar. Figure 6 : High Pressure Fuel Pump for 250bar The new fuel system also contains a customi zed actuator drive box to control the pump solenoid, a host computer , and a MotoTron controller . Figure 7 shows the fuel rail pressure control system . 7 Figure 7 : F uel R ail Pressure Control System 8 CHAPTER 2 : FUEL RAIL SYSTEM DEVELOPMENT 2 .1 Introduction A GDI engine requires a fuel system capable of providing stable high fuel pressure. In this thesis, a fuel rail pressure control system i s developed using a MotoT ron Controller . The MotoTron EC M ( e lectronic control module ) i s synchronized with the motor position using a 60 - 2 tooth wheel and a hall - effect position sensor installed on the motor shaft . The pressure control system inclu des three blocks: I/O definition, fuel rail pressure management system, and CAN communication . A host computer is used for real - time calibration and control tuning . The fuel rail p ressure control system diagram is shown in Figure 8. Figure 8 : Fuel Rail Pressure Control System Diagram 9 The MotoTune is used for calibration and data recording . The intuitive, spreadsheet - like , user interface of the MotoTune make s it easy to access all of the calibration related RAM and ROM parameters contained in the ECM [ 9 ]. The GDI fuel pressure control system is an important part of the engine control system. The lab engine control system uses LabVIEW as the graphic user interface (GUI) . In this thesis, in order to integrate fuel pressure control system into the engine control system, the fuel rail control system communicates with the engine control system through a CAN channel ; and the required information are displayed on the engine co ntrol LabVIEW GUI [10] . In this way , users can tune the fuel pressure control parameters in real - time. A nd the fuel rail pressure is also displayed directly on the engine control LabVIEW GUI. In addition, t he MotoTron fuel pressure controller communicat es with the host computer to make it possible to use the MotoTune through a CAN link. In this c hapter, a mathematical control - oriented model of the fuel rail system i s developed using MATLAB / Simulink. The main fuel rail system model i s based upon the principle of fluid dynamic s . The fuel leak age model i s developed based on the experiment al data and the injector model i s based on the technical data of B osch high pressure GDI fuel injector. T he developed model i s used to characteri ze the fuel rail system and to develop and validate the fuel pressure controller. The control algorithm i s also presented in this c hapter. The fuel rail pressure control strategy consist s of three main parts . They are a b umpless and a nti - windup PI C ontroller , a feed - forward controller , and a dead - zone compensat or . The b umpless and a nti - windup PI and feed - forward controller s are used to minimize the pressure regulation error between the desired and 10 actual fuel rail pressure s . T he dead - zone compensation i s used to preve nt overheating the pump solenoid control valve. 2 . 2 Experiment Equipment 2 . 2 .1 Sensor and Actuator Signal Processing Table 1 and Table 2 list the actuators and sensors used in the control system with their signal definition s . Table 1 : Output Control Signal Definition Signal Definition Type 1 Solenoid c ontrol Position Synchronized PWM Table 2 : Input Control Signal Definition Signal Definition Type 1 Crank position pulse 60 - 2 Hall Sensor 2 Enable/ Disable Boolean 3 Fuel rail pressure 0~5 V 4 Supply pressure 0.88~4.4 V 5 Vcc sense 0~5 V 6 Injector Enable/ Disable Boolean 7 SG_ COM_FuelMass_rk3 N/A 8 SG_ COM_FuelMass_rk2 N/A 9 SG_ COM_FuelMass_rk3 N/A The pressure sensor for the low pressure pump is an industrial pressure transmitter ( GE Druck PTX 7200 Series ) shown in F igure 9 . Supply voltage for the sensor is 9 - 30 V DC; the p ressure range is 0 - 100 psi ; and the o utput signal range is 4 - 20 mA. 11 Figure 9 : Druck PTX 7200 Series I ndustrial P ressure T ransmitter The pressure sensor wire diagram is shown in F igure 10 , which leads to a transfer function for the low pressure sensor as follows : ( 1 ) Figure 10 : Supply Pressure Sensor Wire Diagram The pres sure sensor used for rail pressure is a Chrysler production GDI fuel pressure sensor shown in F igure 11 . Figure 1 1 : Chrysler Fuel Sensor 12 The high fuel pressure sensor wire diagram is shown in F igure 1 2 . Figure 1 2 : High Pressure Sensor Wire Diagram The power supply voltage for the sensor is 4.75 - 5.25 VDC. The operati o n al pressure range is between 0 and 300 bar. The associated tra nsfer function of the sensor is (2) w here (3) 2 . 2 . 2 MotoTune The MotoTune software provides all of the functionalit ies needed for typical calibration tasks. During the system development, the MotoTune is used to display the sensor and control parameter s in real - time and record associated data . More impor tantly, it is used to input real - time control comman ds and calibrations. The MotoTune interface is shown in F igure 1 3 . 13 Figure 13 : MotoTune Interface 14 2 . 2 . 3 CAN Communication CAN communication is very important in the fuel pressure control system. In this research, the first CAN channel is used to compile the auto - coded control algorithm into the MotoTron control module . The MotoTron control module communicates wi th other devices through the second CAN channel as shown in F igure 1 4 . The fuel rail pressure controller sends the control variables , such as pump speed and fuel rail pressure , to the engine controller and display on the engine controller LabVIEW GUI. M eanwhile, the fuel pressure controller can also read the commands from the host computer to calibrate the PI gain s and set reference fuel rail pressure . The CAN li nk between the engine control host computer and the MotoTron controller is through an NI high - speed USB cable. Figure 1 4 : CAN Communication 15 2 . 2 . 4 LabVIEW GUI Development The engine control host computer runs NI LabVIEW GUI. Part of the engine control GUI interface i s used to monitor the fuel rail system status, display the control parameter and sensor values, and provide real - time control commands. The fuel rail system provides the desired fuel rail pressure for the engine system and i t is a part of the entire engine system. Although the fuel rail and engine control system s use different MotoTron control modules , the entire engine system i s monitored and controlled using the same LabVIEW GUI. The monitoring page of the engine control LabVIEW GUI is show n in F igure 1 5 . 16 Figure 1 5 : LabV IEW GUI 17 2 . 3 Fuel Rail System Modeling 2 . 3 .1 High Pressure Pump Model The gasoline direct injection high pressure pump is a single - cylinder , radial - piston pump driven by a camshaft through a roller tappet installed on the engine cam shaft. For this study, the pump is mounted on the electrical motor shaft (simulated cam shaft) . T he pump is driven by the motor shaft with 4 lobes ; see Figure 1 6 for its dimension s . Figure 1 6 : Cam Dimension The pump piston displacement h is dependent on the cam dimension . Let be the camshaft angular position. W hen (2) w hen (3) and w hen 18 (4) The p iston displacement , described by equations (2) to (4) is shown in F igure 1 7 . Figure 1 7 : Piston Displacement In the model, the basic principle of the fuel is expressed by the bulk modulus of elastic ity (see [1 1 ] ) (5) where K f is the bulk modulus of elasticity defined as the ratio of the pressure incre ment to the resulting relative decre ment of the volume and K f and p have the same units bar . Parameter dp is the differential change in pressure ; dv is the differential change in volume ; V is the initial volume; is the differential change in density ; and is initial density. Under normal op erating 19 condition s K f is set to 12,000 bar and its relationship to fuel pressure p (bar) can be express ed as follows [ 1 2 ]: (6) From equation (5), the relationship between the rate changes of pressure and volume can be obtained . (7) The rate change of fuel pressure for the high pressure pump can be written as (8) where is the fuel volume change due to piston motion. (9) (10) According to equation (10), we can have (11) So equation (9) can be rewritten as (12) where is the instantaneous volume of the high pressure pump due to piston motion and it can be calculated by 20 ( 13 ) Note that is the cylinder total volume at BDC and is the section of the pump piston. Let be the intake fuel flow of the high pressure pump , the intake fuel flow of the fuel rail, and the leakage fuel. And can be calculate d by applying the energy conservation law as follows : (14) w here is the supply press ure from the low pressure pump ; is the sign function defining the flow direction ; is the intake orifice section area of the high pressure pump and is the gasoline density ( 0.73kg/L ). F or this study is the coefficient defined as the ratio of the actual discharge to the theoretical discharge [ 1 3] and is chosen to be 0.6. Note that U is the state of the solenoid control valve. When the valve is closed, U = 0 ; and when the valve is open , U = 1 . 2 . 3 . 2 The Fuel Rail The f uel rail contains a certain volume of gasoline fuel. The time derivative of fuel pressure in the fuel rail can be written as ( 15 ) w here is the volume of the fuel rail ; is the leak age due to the pressure relief valve; is the fuel injection flow rate; and is the intake fuel flow of the fuel rail . S ince there is a check valve between the fuel rail and the high pressure fuel pump , the fuel 21 cannot flow back to the outlet of the high pressure pump . Therefore the intake flow can be expressed as follows : (16) w here is the intake orifice section area of the fuel rail. 2 . 3 . 3 Fuel I njector and Leak age The fuel inject ion flow and fuel leakage are considered as perturbations of the fuel rail system and they are determined experimentally . 2 . 3 . 3 .1 Fuel Injector The fuel in jector used in the GDI engine for this study is the high - pressure piezo injec tor HDEV4 made by B osch ; see F igure 1 8 . Figure 1 8 : BOSCH H igh - p ressure Piezo Injector HDEV4 The fuel injector has a high evaporation rate, low penetration , and large metering range. With this injector, the GDI e ngine is able to generate the desired air - fuel mixture directly in the combustion chamber . The technical feature s of the injector are shown in T able 3 . 22 Table 3 : The T echnical F eatures of the I njector Needle actuation Direct Spray angle 85 °± 5 ° Shot - to - shot scatter ± 1 ° Back - pressure dependence < 4% Droplet size SMD (Sauter Mean Diameter) 10 - 15 m Penetration < 30 mm Needle lift 35 m Partial - lift capability 10 - 35 m I njection time 70 - 5000 s Multiple injection 5 injections/cycle Interval time 50 s Metering range 0.5 - 150 mg/injection The dynamic flow range of the injector is ( 34.5 mg/lift @ t=1ms ) . For the test engine, t here are 3 injection s available for each combustion event as shown in T able 4 . Table 4 : Injection Signals Function Name Units DI Fuel Mass Injection1 % Inject ion2 % Injection3 % The total inje ction flow can be calculated by (17) 2 . 3 . 3 .2 Leak age The leak age flow is caused by the pressure relief valve used to prevent over - pressuriz ing the fuel system . When the pressure is lower than 200 bar, the leakage flow is very small and can be neglected . When the pressure is higher than 200 bar, the relationship between leak age flow 23 and pressure are nonlinear . In the model, the leakage flow is calculated by using a lookup table that represents the nonlinear relationship between the pressure and leakage flow . T he data in the lookup table were determined experimentally an d they are shown in F igure 1 9 . Figure 1 9 : Relationship between the Leakage and the P ressure 2 . 4 Fuel Pump Control 2.4.1 Control Principle The open - loop control strategy of the high p ressure fuel pump is shown in F igure 20 . The cam is driven by the electrical motor shaft (simulated cam shaft) so that the piston of the high pressure fuel pump move s up and down. For safety reason s , the solenoid control valve inside the pump is normally open. When the piston moves downward from the top dead centre (TDC) to the bottom dead centre (BDC), the fuel flows into the high pressure fuel pump from its intake port due to the pressure d ifference. The demand control valve inside the high pressure pump is activated by the solenoid so that the flow volume can be regulated between zero and maximum delivery. When the piston moves upwards from BDC to TDC, the solenoid control valve is closed f or a certain time period t that is the control variable for the fuel pressure control system. 24 During this time period , the piston goes up and pushes the fuel from the outlet into the fuel rail. A fter this time period , the solenoid control valve open s again . Due to the check valve between the fuel pump and rail , the fuel cannot flow back to the outlet , the fuel pressure inside the fuel rail can be maintained . Since the piston keeps moving up due to the pressure difference , the fuel flows back to the fuel tank from the high pressure pump through the intake valve. Figure 20 : Control Principle of the High Pressure Fuel Pump The whole fuel pump system i s synchronized with the motor shaft position signal. Since a MotoTron engine controller is used for fuel pump control, one engine cycle in the MotoTron is 720 ° . For our case the pump is mounted on the equivalent crankshaft with each rotation equal to 36 0 °, which leads to four strokes for the fuel pump. Within one engine cycle in the MotoTron control module , 8 control pulses need to be generated for the pump sole noid valve as shown in 25 F igure 2 1 . Channel 1 (C1) , the yellow signal, is the simulated cam posit ion signal (one pulse per engine cycle); c hannel 2 (C2) , the pink signal, is the electric motor shaft position (simulated crank) single (60 - 2 tooth ); and c hannel 3 (C3) , the blue signal, is the generated control pulse signal for the solenoid control valve. The pulse width is the control variable that will be defined by the output of the duel rail pressure controller. In this study, the dSPACE engine simulation system is used to simulate the crank position pulse signal with 60 - 2. Figure 2 1 : Pulse Signal for Solenoid Control Valve Synchronized with Crank Position Pulse To have high pumping efficiency, the rising edge of the solenoid valve control pulse should begin at the pump BDC. The control pulse without proper calibration is shown in F igure 2 2 . 26 Figure 2 2 : Pulse Signal for Solenoid Control Valve before Calibration The BDC location i s determined after the pump i s installed on to the motor shaft . From F igure 2 2 , the start of the pulse sig nal is obviously after the BDC . B y moving the pulse signal forward the rising edge can be in - line with the BDS as shown in F igure 2 3 . Figure 2 3 : Pulse Signal for Solenoid Control Valve after Calibration 27 2 . 4 . 2 Open - Loop Control The open - loop control system, shown in the F igure 2 4 , does not include any feedback signal . Figure 2 4 : Open - l oop Control System Although the open - loop control cannot correct any pressure regulation errors and compensate for disturbances in the fuel system , it was used to observe the relationship between the control input and pressure response. T he open - loop control test results are us ed to generate certain calibrations for the close d - loop controller. 2 . 4 . 3 Close d - Loop Control The c lose d - loop control aim s to minimize the error between the actual fuel rail pressure and the des ir ed ( reference ) pressure . The closed - loop control system structure is shown in F igure 2 5 . T he close d - loop controller in this research contains a PI con troller with the dead - zone compensation. Figure 2 5 : Close d - l oop Control System 28 2 . 4 . 3.1 PI Controller In this study, a bumpless anti - windup PI controller i s used to control the fuel rail pressure . The PI controller is shown in F igure 2 6 . T he feed - forward block of this PI controller can be used for future feed - forward control . T he proportional gain block of the PI controller includes a bumpless gain feature , which limits the rate of change of the proportional gain to provide smooth gain scheduling ; and the PI control system further includes anti - windup logic to disable the PI integrator if the actuator drive signal is upper or lower bounded and the error signal is greater or less than zero respectively, thereby creating dynamic saturation of the PI integrator [ 14 ] . Figure 2 6 : B umpless and A nti - windup PI C ontroller The solenoid drive circuit has a 1.0 ms precharge feature to improve the repeatability of the pump solenoid valve and it is validated d uring the open - loop control test . That is, when the pul se width i s smaller than 1 .0 ms, the solenoid control valve d oes not react to the control pulse . Therefore, the control pulse lower and upper bond s are set to 1. 0 and 1.2 ms respectively to avoid the PI controller integrator over flow and reduce pressure overshoot. 29 2 . 4 . 3.2 Dead - z one Compensation Due to the electro - magnetic property of the solenoid valve , it takes about 0.3 ms to open after the pulse rising edge; and it takes even more time to close the solenoid control valve. The time delay between the open and close of the solenoid control valve is defined as the dead - zone shown in F igure 2 7 . Figure 2 7 : Dead - zone Definition As a summary, when the control pulse width is smaller than 1 ms, the solenoid valve will not open , but there is current flow through the solenoid winding , which could increase the solenoid winding temperature. The dead - zone compensation is to set the pulse width to 0.1 ms w hen the PI control p ulse width is smaller than 1 ms and the output is equal to the PI control pulse width when the PI control i s greater than or equal to 1 ms. The seventh and eighth input s ( IntInit and IntReset ) in the bumpless and anti - windup PI controller are used to implement the dead - zone compensation . IntReset i s connected with the enable/disable of the solenoid control pulse signal. The input of IntInit was set as 1.0 ms so that t he PI controller respon ds faster. 30 2 . 4 . 4 Feed - f orward Control Feed - forward control is used to compensate the fuel leak age and injection flow . If t he PI controller consisted of the bumpless and anti - windup feature with dead - zone compensation , the fuel rail pressure w ould fluctuate significantly. For example, when the desired pressure i s 200 bar, the actual fuel rail pressure fluctuat ion i s shown in F igure 2 8 , where the large decreasing of the fuel pressure is caused by the start of fuel injection . F igure 2 8 shows that the fuel rail pressure drops around 12 bar after fuel injection starts and the control sys tem response is slow without feed - forward control . Although the pressure i s stable at the steady state with an error between the reference and actual fuel rail pressure less than 2%, the huge pressure drop needs to be avoided. B y adding the feed - forward control, the fuel rail pressure fluctuation during the transient operation can be improved significantly . Figure 2 8 : Experiment Data of the Pressure Performance of the System without Feed - f orward C ontrol with injection The feed - forward controller attempts to compensate the fuel leak age and inject ion flow. T he max flow injection quantity is 4.7 × 10 - 8 m 3 per lift at 1ms . The volume change d ue to piston motion is shown in F igure 2 9 . 31 Figure 2 9 : Volume C hange d ue to P iston M otion from 0 to 1.2ms Because of the dead - zone, the solenoid is a ctive only from 1 ms to 1.2 ms. Hence , the max imum volume of the flow from the pump to the fuel rail is 0.48 × 10 - 8 m 3 per pulse. According to the relationship between piston position and output flow v olume, a feed - forward lookup table , shown in T able 5 , can be designed . For e very simulated engine cycle , there are eight pulses to control the solenoid control valve to compensate the injection volume. When the injection flow volume increase s , the pulse width can exceed 1.2 ms. Table 5 : Lookup Table for Feed - forward Control Compensation Flow Volume (m 3 ) Pulse width (ms) 0 1 0.0454 × 10 - 8 1.02 0.0908 × 10 - 8 1.04 0.1362 × 10 - 8 1.06 0.1817 × 10 - 8 1.08 0.2302 × 10 - 8 1.10 0.2794 × 10 - 8 1.12 32 Table 5 (cont d) 0.3286 × 10 - 8 1.14 0.3777 × 10 - 8 1.16 0.4294 × 10 - 8 1.18 0.4824 × 10 - 8 1.20 33 CHAPTER 3 : S I MULATION VALIDATION 3 .1 Introduction Simulation v alidation of the developed s imulation m odel is conducted during the model development process to ensure the model accura cy [ 15 ] . The model was developed using the se parameters measured on the actual fuel rail system and calibrated by comparing the Simulink model response with the experiment al data . Two different operating conditions a re simulated to validate the control law : o ne is for tracking validation and a nother for tracking with injection flow . These two validation conditions are also repeated in the experiment s . The Simulation results show that the fuel rail control system is able to maintain the fuel rail pressure with or without fuel leakage and injection flow disturbance s . Before the controller could be used on the actual fuel rail system, it should be validated using the simulation model. After the model was developed , the s imul ation and experiment data were compared , which is described in the next C hapter. 3 . 2 Model Validation Simulation validation is utilized to determine if the developed model is an accurate representation of the actual system [1 6 ]. To test the fuel rail pressure, a fuel rail plant model was established in Simulink. The parameters of the fue l rail system are shown in T able 6 . With these parameters, the fuel rail system Si mulink model is able to replicate characteristics of t he actual fuel rail system. 34 Table 6 : The Parameters in GDI Fuel Rail System Simulink Model The section of the inlet in high pressure pump (m 2 ) 1.69 × 10 - 5 The section of the inlet in fuel rail (m 2 ) 1.65 × 10 - 5 The section of the pump piston (m 2 ) 6.33 × 10 - 5 The max volume of the high pressure pump (m 3 ) 8.7 × 10 - 7 The pressure supplied by low pressure pump (psi) 32 Solenoid valve delay time (ms) 2.5 The volume of fuel rail (m 3 ) 8 .3 × 10 - 5 Motor Speed (RPM) 1200 D ensity of the Gasoline (kg/L) 0.73 The fuel rail Simulink model is shown in F igure 30 . The block diagram of the close d - loop fuel rail system with the controller is shown in F igure 31 . Figure 30 : Fuel Rail System Simulink Model 35 Figure 31 : The Block Diagram of the Close d - loop Fuel Rail System with Controller From the control principle, it is obvious that when the solenoid control valve is closed, the intake flow is zero. When the control valve is open, the output flow will be zero. T he relat ionship of intake flow and output flow w ith a 1.2 ms control pulse is shown in F igure 32 . 36 Figure 3 2 : Relationship among Each Signal Two different condition s are simulated using Simulink software to validate the control law. The first is the pressure tracking without fuel injection ; and the second is the pressure tracking with fuel injection. 3 . 2 . 1 Tracking Validation In this part, two desired pressure s 200 bar and 250 bar , a re used to validate the model and the developed controller. I n the bumpless and anti - windup PI controller, the P gain is 0.005 and I gain is 0.035. The simulation result with 200 ba r desired fuel pressure is shown in F igure 3 3 . It takes about 3 seconds to reach 200 bar and t he peak error is within 1 %. 37 Figure 3 3 : Simulation Result with the Desired Pressure of 200bar. The simulation result for the case of 250 bar desired pressure is shown in F igure 3 4 . W ithin 3.5s, the pressure reaches 250 bar with a max error of 0.6%. Figure 3 4 : Simulation Result with the Desired Pressure of 250bar 38 3 . 2 . 2 Fuel Inject Flow Compensation In the Simulink simulation , a fuel inject ion signal is added to study the performance of the feed - forward controller. T he i njection pulse width is 1 .0 ms at the engine speed of 1200 RPM . When the desired fuel pressure i s 200 bar without the feed - forward control, the fuel rail pressure drops to 170 bar as shown in F igure 3 5 . Figure 3 5 : Injection without Feed - f orward Controller at 20 0bar From the simulation result shown in F igure 3 5 , it is obvious that without the feed - forward controller, when the fuel injection start s the fuel rail pressure drop s significantly. That could lead to inaccurate fuel injection under the transient engine operational conditions . The fuel rail pressure regu lation under transient fuel injection with the feed - forward controller is shown in F igure 3 6 . The fuel rail pressure error i s less than 0.05%. 39 Figure 3 6 : The Pressure Perfo rmance of the S ystem with Feed - f orward Control with I njection at 200bar The fuel rail pressure under the fuel injection perturbation with the feed - forward controller at 250 bar is shown in F igure 37 , where fuel rail pressure error is less than 0.05%. Figure 3 7 : The Pressure Perfo rmance of the S ystem with Feed - f orward Control with I njection at 250bar 40 CHAPTER 4 : EXPERIMENTAL VALIDATION 4 .1 Introduction Although the simulation model is able to demonstrate the characteristics of the fuel rail systems, it will never imitate the exact real - world system. It i s necessary to validate the whole system experiment ally . In this C hapter, the fuel rail system i s validated without fuel injection perturbation . In the meantime, the Simulink simulation result s are compared with the experiment data. 4 . 2 Tracking Validation The controller parameter s used in the experiments are the same as th ose used in the simulations . Without fuel injection, the compar ison of the experiment al and simulation result s are shown in F igure 3 8 and F igure 3 9 . Figure 3 8 shows the comparison when the desired fuel rail pressure i s 200 bar. Within 3 seconds, the fuel rail pressure reache s 200 bar with a steady - state error of 0.9%. Figure 3 8 : C omparison of the E xperiment R esult and Simulink R esult at 200bar 41 Figure 3 9 shows the case of 250 bar desired fuel rail pressure. Within 5 s econds , the fuel rail pressure reache s 250 ba r with a max steady state - error of 0.8 %. The error between the simulation result (blue line) and the experiment data (red dot) i s less than 2.5 % at the steady state . Figure 3 9 : C omparison of the E xperiment R esult and Simulink R esult at 250bar 4 . 3 Leak age Protection Since the pressure relief valve of the fuel rail system causes certain fuel leak age near the fuel pressure of 250 bar , the fuel rail pressure varies due to the leakage flow . H owever, with the help of the close d - loop control, the pressure is maintain ed at the desired pressure. Figure 40 shows the fuel rail pressure trace when the desired fuel pressure i s 250 bar. The maximum rail pr essure i s 252.3 b a r, and the minimum i s 248.2 bar , which leads to a steady - state error of less than 1%. 42 Figure 40 : Leak Protection at the Desired Pressure at 250bar 43 CHAPTER 5 : CONCLUSIONS AND FUTURE WORK 5 . 1 Conclusions In this thesis, a fuel rail control system i s developed. The whole system i s developed based upon a Moto T ron engine control module (ECM) . LabV IEW GUI i s used as the user graphic interface. T he control system i s calibrated using the MotoTune software . T he MotoTron ECM communicate s with the MotoTune and Lab VIEW GUI through its CAN link s . To meet the fuel rail pressure control requirements of a GDI engine fuel system, in this thesis, a control - oriented mathematical model of a fuel rail system for a GDI engin e i s developed using MATLAB / Simulink. The Simulink model i s then used to develop and validate the pressure control strategy before the pressure controller i s validated experiment ally . B y comparing the experiment data, the simulation results show that the mathematical model is able to replicate the behavior of the actual fuel rail system. The pressure control strategy of the fuel rail system con sists of three parts : a b umpless and a nti - windup PI C ontroller , a feed - forward controller , and a dead - zone compensat or . By validating the pressure controller both in simulations and experiment s , the control strategy is validated. A nd the closed - loop controller is able to meet the fuel pressure regulation requirements. 5 . 2 Future Recommendations In this thesis , the fuel rail system is able to maintain the fuel rail pressure at the desired pressure with or without the fuel injection perturbation . H owever, the fuel system efficiency and performance i s not considered and it c ould be im proved through further calibration s of the start 44 position of solenoid control pulse or decreas ing the number of pulses. The fuel rail control system can be further improved by using advanced control strategies . For the effect of fuel injection, it is important to validate it experimental ly and additional control calibration s would be required . 45 APPENDI CES 46 A PPENDIX A Fuel Pump Harness Figure 41 : Fuel Pump Harness 47 A PPENDIX B MotoT ron Simulink Diagram Figure 42 : MotoTron Simulink Diagram 48 REFERENCES 49 REFERENCES [1] U. Spicher , J . Reissing , J. M. Kech and J. Gindele Gasoline Direct Injection (GDI) Engines - Development Potentialities , SAE International , 19 99 (doi: 10.4271/ 1999 - 01 - 2938 ) . [2] Autuan Goodwin What s so Great about Direct Injection ABCs of Car Tech [3] R. Morselli, E. Corti and G. Rizzoni, Energy B ased M odel of a C ommon R ail I njector, Proc. O f the 2002 IEEE Int. Conf. on Control App, Glasgow, Scotland, September 2002 , pp. 1195 - 1200 [4] P. Lino, B. 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