251‘s (2‘ 5 b Immm‘m’lfl”m»“LilliImulllml 293 00575 6881 UBRARY e Michigan State University This is to certify that the dissertation entitled Adaptive control of continuous-flow ra1n dr ers pgesentedby 'y Rosana Galves Moreira has been accepted towards fulfillment of the requirements for Doctoral degree in AE % 612/ a; 'Major professor Date/12%? MS U is an Ajfmnative Action/Equal Opportunity Institution 0- 12771 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before due due. DATE DUE DATE DUE DATE DUE MSU Is An Affirmative Action/Equal Opportunity Institution ADAPTIVE CONTROL.OP CONTINUOUS FLOW GRAIN DRYERS BY Rosana Calves Moreira A.DISSERIAIION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR.0P PHILOSOPHY IN Agricultural Engineering Department of Agricultural Engineering 1989 I L/ ABSTRACT ADAPTIVE CONTROL OF CONTINUOUS FLOW GRAIN DRIERS BY Rosana Calves Moreira Adaptive control was evaluated as a tool for continuous-flow grain dryer control. The highly complex dynamics of the dryer provides an ideal test for adaptive control. An adaptive control technique based on a continuously updated linear controller was developed. A control system was implemented and tested during two drying seasons on two commercial crossflow dryers. The system consists of a linear model, a control algorithm, an on-line moisture meter, a tachometer and a microcomputer. The outlet grain moisture content was controlled to within £0.3t of the setpoint even for a large variation in the inlet moisture content. An unsteady-state model of concurrentflow corn drying was developed consisting of four differential equations. The model was used to simulate the automatic control of a two-stage CCF dryer. Five different empirical models were developed for describing the dynamics of the drying process. The best results were obtained with the Model II-b. Two different adaptive controllers were used in both the experimental and theoretical parts of this study: (1) a generalized minimum variance controller (GHV) based on a time-series linear model and, (2) a pole placement controller (PP) based on an integrated moving average linear model. The best control performance was obtained with the PP- controller, the worst with the HV-feedforward controller. The MV- feedback/feedforward controller also gave good results but it reacted too slowly for large variations in the inlet moisture content. The PP-adaptive controller can be adopted to any dryer and grain type. It is stable, accurate, and has a quick response. It is recommended for any continuous-flow grain dryer automatic control. Approved Major Professor Approved Department Chairman To my unforgettable Grandmother Dolores Peres (May/1898-June/l988) iv ACKNOWLEDGMENTS I am deeply indebted to Dr. Fred W. Bakker-Arkema for sugges- tion of the research topic and his continuous support, interest, and patient guidance throughout the course of this study. Sincere appreciation is extended to the guidance comittee members: Dr. Roger C. Brook, Agricultural Engineering Department; Dr. Kris A. Berglund, Department of Agricultural Engineering and Chemical Engineering and Dr. Robert O. Barr, Department of Electrical Engineering and Systems Science. Special thanks goes to Fernado A. Osorio and Dr. Abbas Y. Eltigani for their help and moral support. Special thanks is extended to Paul Maag and Sons, Inc. (Eagle, MI) and Anderson Grand River Grain Terminal (Webberville, M1) to allowing me to use their drying facilities. To the entire Processing Group and the Graduate students of the Agricultural Engineering Department, Michigan State University, a spe- cial thanks for the encouragement and support. Deepest appreciation goes to my mother Odette G. Moreira for her love, sacrifices and encouragement; to the Castell family, to my sister Walkiria, my brother Marcos, my aunt Rosaria M. Galves and my friend Ann for their moral support. I specially wish to express my gratitude to my good friend Elena for her friendship, help, words of encouragement and continuous support which I will never forget. Special thanks and appreciation is sincerely expressed to the Brazilian Government for financial support during part of this study. ”...Every acquisition, every step forward in , knowledge, is the result of courage, of severity towards oneself, of cleanliness with respect to oneself..." (F.Nietzsche, Ecce Homo) vi TABLE OF CONTENTS LIST OF TABLES .................................................... LIST OF FIGURES ................................................... LIST OF SYMBOLS ................................................... CHAPTER 1. INTRODUCTION ................................................... 2. OBJECTIVES ..................................................... 3. LITERATURE REVIEW .............................................. 3.1 GRAIN DRYING SYSTEMS ....................................... 3.1.1 Crossflow Dryers ..................................... 2 Concurrentflow Dryers ................................ 3 Counterflow Dryers ................................... 4 Mixed- Flow Dryers .................................... 5 Other Dryer Types .................................... 1 Thin- -Layer Drying Equations .......................... 3.2.1.1 Discussion of the Drying Equations ........... 2 Deep- -Bed Drying Models ............................... 3. 2.2.1 Continuous- flow Grain Dryer Models ........... 3.2.2.2 Other Drying Types Models .................... 3.1. 3 1. 3.1. 3.1. 3.2 MATHEMATICAL MODELING OF CONTINUOUS FLOW GRAIN DRYERS ...... 3. 2. 3. 2. 3.3 CONTROL SYSTEMS ............................................ 4. THEORY ........................................................ 4.1 CONTINUOUS-FLOW GRAIN DRYER CONTROL DESIGN ................. 4.1.1 Drying Process Models ................................ 1 Time- Series Model I .......................... 2 Time- Series Model II-a ....................... 3 Time- Series Model 11- b ....................... 4 Linear Model ................................. 5 Exponential Model ............................ eter Estimation ................................. mpling Strategy .................................... ontrol Algorithm .................................... .1. 4. l Generalized Minimum Variance Controller- (GMV) Hidrdhihnu .1. .1. .1. .1. .1. am t‘knfi P‘PHH bio?» eommebeeb Page X xii xvi 1 6 67 67 4.1.4.1.1 Minimum Variance Feedback Controller 68 4.1.4.1.2 Minimum Variance Feedforward Controller ........................... 69 4.1.4.1.3 Minimum Variance Feedback/feedforward Controller ........................... vii 7O 4.1.4.1.4 Offset Compensations for Minimum Variance Controllers ................. 4.1.4.2 Pole Placement Controller-(PP) .............. 4.1.4.3 Model-Based Controller-(MB) ................. 1.5 Filtering of the Parameter Estimation ................ 1.6 Control Algorithm Flow Diagram ....................... 4. 4. 4.2 UNSTEADY-STATE CONCURRENTFLOW DRYING ....................... 4.2.1 Development of the Unsteady-State Model .............. 4.2.2 Numerical Solutions .................................. 5. EXPERIMENTAL.INVESTIGATION ..................................... 5.1 CONTROL OF CROSSFLOW GRAIN DRYERS .......................... 5.1.1 Equipments ........................................... 5.1.2 Control System ....................................... 5.1.3 Procedure ............................................ 5.2 CONTROL OF MULTI-STAGE CONCURRENFLOW GRAIN DRYERS .......... 5.2.1 Two-Stage Concurrentflow (CCF) Dryer ................. 5.2.2 Procedure ............................................ 5.3 NUMERICAL IDENTIFICATION ................................... 6. RESULTS AND DISWSSICE ......................................... 6.1 CROSSFLOV DRYING PROCESS ................................... 6.1.1 Model Identification Results ......................... 6.1.1.1 Numerical Identification of the Meyer-Morton Dryer ........................................ 6.1.1.2 Numerical Identification of the Zimmerman Dryer ........................................ 6.1.2 Control Results ...................................... 6.1.2.1 Meyer-Morton 850 Dryer ....................... 6.1.2.2 Zimmerman ATP 5000 Dryer ..................... 6.2 CONCURRENTFLOV DRYING PROCESS .............................. 6.2.1 Model Identification Results ......................... 6.2.1 Concurrentflow Dryer Control ......................... 6.2.1.1 Randomly Distributed Step Input Signal ....... 6.2.1.2 Ramp Input Signal ............................ 6.3 DISCUSSION ................................................. 6.3.1 Implementation ....................................... 6.3.2 Application to Other Dryer Types ..................... 7. SUMMARIHAND OOHCUUSIONS ........................................ 8. SUGGESTIONS FOR.FUTURE STUDY ................................... 9. REFERENCES ..................................................... 10. APPENDICES .................................................... APPENDIX A - Derivation of the GMV Controllers ................ APPENDIX B - Description of the Procedure to Determine the viii 97 99 104 105 105 111 114 114 114 115 118 122 122 133 141 151 162 164 182 188 192 193 195 197 198 206 206 Relationship Between RPM and Residence Time for Continuous-flow Grain Dryer .................. 210 ix TABLE 1.1 O‘U‘UlU‘ HUMP LIST OF TABLES Page Production of cereal crops and soybeans by region in 1986 (million tonnes) ....................................... 1 Production of corn, soybeans and wheat from 1979-1986 (million tonnes) in Brazil and USA .......................... 2 Maximum and optimum moisture content (%w.b.) for grains at harvest and safe storage .................................... 4 Experimental results of the drying of corn in a crossflow dryer with air recirculation and air-reversal ............... 13 Experimental results of the drying of corn in a crossflow dryer with air recirculation, differential grain speeds and tempering ................................................... 13 Experimental results of the drying of long—grain rice in a two-stage CCF dryer ......................................... 18 Experimental results of the drying of soybeans in a mixed- flow dryer .................................................. 19 Performance data of three-rotary dryer system in a rice parboiling plant ............................................ 22 Performance data of the drying of wheat in a spouted-bed dryer with a counterflow cooler ............................. 26 Shrinkage in bushel and cost resulting from various levels of overdrying of 25,401.6 tonnes of 15.5t w.b. corn ......... 42 Energy required and cost resulting from various levels of overdrying of 25,401.6 tonnes of 15.5% w.b. corn ............ 43 Physical properties of air and corn used in the unsteady- state simulation model ...................................... 89 Meyer-Morton 850 crossflow dryer specifications ............. 94 Zimmerman ATP 5000 crosflow dryer specifications ............ 96 Blount/cdd two-stage CCF dryer specifications ............... 107 Parameter valus for the model I and model II-b models of the Meyer-Morton dryer ................................... 117 Summary of the results obtained from the different control tests with the Meyer-Morton 850 dryer ....................... 134 .10 .11 .12 .13 .14 Summary of the results obtained from the different control tests with the Zimmerman ATP 5000 dryer ..................... 140 Simulation input parameters for the single-stage CCF dryer.. 141 Steady-state results for the two-stage of a CCF dryer predicted by the steady-state (SS) and unsteady-state (USS) models ...................................................... 145 Steady-state results for the lst-stage of a CCF dryer predicted by the steady-state (SS) and unsteady-state (USS) models ...................................................... 146 Differences between the SS model and the USS simulation models ...................................................... 147 Simulation input parameters for the two-stage CCF dryer ..... 149 Estimates for the model I, model II-a, model II-b [Eqns.(4.2), (4.3) and (4.4), respectively] .............................. 155 Estimates for the linear model and exponential model [Eqns. (4.6) and (4.7), respectively] .............................. 155 Inlet moisture content sets used as input in the simulation of a two-stage CCf grain dryer .............................. 163 Characteristic values of the different control performances with the inlet moisture content variation from Setl and setpoint equal to 16$ w.b ................................... 173 Characteristic values of the different control performances with the inlet moisture content variation from Setl and setpoint equal to 17% w.b ................................... 181 Characteristic values of the different control performances with the inlet moisture content variation from Set2 and Set3 and, setpoint equal to 16‘ w.b .............................. 187 xi FIGURE .k www NNH “WWW kWh-7N buyout-aw LIST OF FIGURES Page Grains production in Brazil from 1950-1986 ................. 3 Schematic of the four basic types of continuous-flow dryer. 9 Moisture and temperature changes during crossflow drying... ll Moisture and temperature changes during concurrentflow drying ..................................................... 11 Moisture and temperature changes during counterflow drying. 11 Moisture and temperature changes during mixed-flow drying.. 11 Crossflow dryer with forced-air drying and cooling ......... 12 Schematic of 3-stage crossflow dryer with partial air recycling .................................................. 12 Schematic of a crossflow dryer with differential grain-speed and tempering .............................................. l4 Schematic of a two-stage concurrentflow grain dryer with counterflow cooler and air recycling ....................... 16 Schematic of a mixed-flow grain dryer ...................... 20 Distribution of air in the ducts of a mixed-flow dryer ..... 20 Concurrenfow rotary dryer .................................. 23 Fluidized-bed dryer ........................................ 25 Spouted-bed dryer .......................................... 25 Identification of dryer segments and grain layers considered in the linear model of the continuous-flow grain drying.... 60 Control algorithm for continuous-flow grain dryers ......... 78 Energy and mass balances on a control volume within a concurrenflow grain dryer .................................. 81 Schematic of the Meyer-Morton 850 crossflow dryer .......... 93 Schematic of the Zimmerman ATP 5000 crossflow dryer ........ 95 Schematic of the adaptive control system for the crossflow dryer ...................................................... 98 xii .10 .11 .12 .13 .14 .15 .16 .17 Schematic of a two-stage CCF dryer ......................... 106 Meyer-Morton experimental data employed to obtain the parameters of model I and model II-b ...................... 116 Identification results with the first-order model I for the drying of corn in the Meyer-Morton 850 dryer ............... 119 Identification results with the second-order model I for the drying of corn in the Meyer-Morton 850 dryer ............... 120 Identification results with the first-order model II-b for the drying of corn in the Meyer-Morton 850 dryer ........... 121 Zimmerman experimental data employed to obtain the parameters of model I and model II-b ...................... 123 Identification results with the linear model (Equation 4.6) for the drying of corn in the Zimmerman ATP—5000 dryer ..... 124 Results obtained during manual control of the Meyer-Morton 850 dryer (1984) ........................................... 126 Results obtained during manual control of the Meyer-Morton 850 dryer (1985) ........................................... 127 Results of Testl obtained during automatic control of the Meyer-Morton 850 dryer with the MV-feedback controller ..... 128 Results of Test2 obtained during automatic control of the Meyer-Morton 850 dryer with the MV-feedback controller ..... 129 Results of Test3 obtained during automatic control of the Meyer-Morton 850 dryer with the MV-feedback/feedforward controller ................................................. 130 Results of Test4 obtained during automatic control of the Meyer-Morton 850 dryer with the MV-feedback/feedforward controller ................................................. 131 Results obtained during manual control of the Zimmerman ATP 5000 dryer (1987) .......................................... 136 Results of Tests obtained during automatic control of the Zimmerman ATP 5000 dryer with the PP-controller ............ 137 Results of Test6 obtained during automatic control of the Zimmerman ATP 5000 dryer with the PP-controller ............ 138 Steady-state temperature and moisture profiles for the 2nd-stage of a CCF dryer predicted by the steady-state (SS) and the unsteady-state (USS) models ........................ 143 Steady-state temperature and moisture profiles for the 2nd-stage of a CCF dryer predicted by the steady-state (SS) xiii .18 .19 .20 .21 .22 .23 .24 .25 .26 .27 .28 .29 .30 .31 .32 .33 .34 and the unsteady-state (USS) models ........................ Steady-state temperature and moisture profiles for the lat-stage of a CCF dryer predicted by the unsteady-state model for different grain flow rates ...................... Steady-state temperature and moisture profiles for the two stages of a CCF dryer predicted by the unsteady-state model ...................................................... Unsteady-state moisture profile for the two stages of the CCF dryer at constant GFR .................................. Unsteady-state moisture profile for the two stages of the CCF dryer at varying GFR ................................... Identification results with the first-order model I for the drying of corn on a two-stage CCF dryer .................... Identification results with the second-order model I for the drying of corn on a two-stage CCF dryer ................ Identification results with the model II-a for the drying of corn on a two-stage CCF dryer ........................... Identification results with the model II-b for the drying of corn on a two-stage CCF dryer ........................... Identification results with the linear model for the drying of corn on a two-stage CCF dryer ........................... Identification results with the exponential model for the drying of corn on a two-stage CCF dryer .................... Simulation of the automatic control of a two-stage CCF dryer (no control) ......................................... Simulation of the automatic control of a two-stage CCF dryer using the PP-controller .............................. Simulation of the automatic control of a two-stage CCF dryer using the MV-feedback/feeforward controller .......... Simulation of the automatic control of a two-stage CCF dryer using the MV-feedback controller ..................... Simulation of the automatic control of a two-stage CCF dryer using MV-feedforward controller ...................... Simulation of the automatic control of a two-stage CCF dryer using MB-controller .................................. Simulation of the automatic control of a two-stage CCF dryer using PP-controller ................................. xiv 144 148 150 152 153 156 157 158 159 160 161 167 169 169 170 171 172 176 .35 .36 .37 .38 .39 .40 .41 .42 .43 .44 Simulation of the automatic control of a two-stage CCF dryer using MV-feedback/feeforward controller .............. 177 Simulation of the automatic control of a two-stage CCF dryer using the MV-feedback controller ..................... 178 Simulation of the automatic control of a two-stage CCF dryer using MV-feedforward controller ...................... 179 Simulation of the automatic control of a two-stage CCF dryer using MB-controller .................................. 180 Simulation of the automatic control of a two-stage CCF dryer (no control, Set2) ................................... 184 Simulation of the automatic control of a two-stage CCF dryer (Set2) using PP controller ........................... 185 Simulation of the automatic control of a two-stage CCF dryer (Set2) using MV-feedback/feedforward controller ...... 186 Simulation of the automatic control of a two-stage CCF dryer (no control, Set3) ................................... 189 Simulation of the automatic control of a two-stage CCF dryer (Set3) using PP controller ........................... 190 Simulation of the automatic control of a two-stage CCF dryer (Set3) using MV-feedback/feedforward controller ...... 191 LIST OF SYMBOLS 1 a specific surface area, m- ca air specific heat, kJ/kg-°C cp product specific heat, kJ/kg-°C cv vapor specific heat, kJ/kg-°C cw water specific heat, kJ/kg-°C D diffusion coefficient, mz/hr Ga air flow rate, kg/hr-m2 Gp grain flow rate, kg/hr-m2 h' convective heat transfer coefficient, kJ/hr-m2-°C f8 latent heat of vaporization , kJ/kg M moisture content, decimal d.b. r radius, m T air temperature, °C t time, minute or hour Va air velocity, m/hr Vp product velocity, m/hr W absolute humidity of air, kg water/kg dry air x coordinate direction along the length of the dryer, m Greek Symbols 0 grain temperature, °C e bed porosity pa air density, kg/ms pp dry weight product density, kg/m3 CHAPTER 1 Grains are the major source of food for human and animals throughout the world. Grains include mainly: (1) cereal grains (wheat, corn, rice, barley, sorghum, millet), (2) the oil seeds (soybeans, canola seed, sunflower seed) and (3) legume grains (edible beans, peas). Grains are grown in all parts of the world. Table 1.1 lists the annual world-wide production of the main cereal grains and of the most important oil seed (soybeans). Table 1.1: Production of cereal crops and soybeans by region in 1986 (million tonnes). Area Wheat Rice Corn Millet Barley Sorghum Soybeans Africa 11.6 9.8 30.8 11.8 6.3 14.3 0.4 North America 93.5 8.3 231.3 ---- 28.7 30.4 56.4 South America 16.8 15.3 38.2 0.1 0.8 6.2 21.3 Asia 189.6 434.1 99.7 15.3 18.7 17.4 15.4 Europe 115.8 2.2 68.0 0.03 70.3 0.4 1.6 Source: FAO (1987) Wheat, rice and corn are the major crops, in terms of tonnage. Asia raises the most wheat and rice. The American Continent is the major producer of corn, sorghum and soybeans. Barley is most popular in Europe, while millet is in Asia and Africa. In South America, Brazil is one of the most important grain producers. In Brazil, only 10% of the total land (851 million hectares) is used for agricultural production (FAO, 1987). About 80% of this total land is concentrated in the Southeast and South of Brazil where the agriculture system is almost completely mechanized. The major grains grown in Brazil are corn, rice, wheat, soybeans and dry beans. Rice and dry beans are the staple foods in Brazil; Table 1.2 shows the 1979-1986 production of corn, rice, soybeans and wheat in Brazil and USA. Table 1.2: Production of corn, rice, soybeans and wheat from 1979-1986 (million tonnes) in Brazil and USA. Year Country Corn Rice Soybeans Wheat 1979-81 Brazil 19.3 8.5 13.5 2.8 USA 192.0. 7.0 56.1 66.2 1984 Brazil 21.2 9.0 15.5 2.0 USA 194.9 6.3 52.3 66.0 1985 Brazil 22.0 9.0 18.3 4.3 USA 225.5 6.1 59.1 65.9 1986 Brazil 20.5 10.4 13.3 5.4 USA 209.6 6.1 56.3 56.8 Source: FAO (1987) From 1979-1985, the production of corn had an increase of 14% in Brazil and an increase of 17% in the United States; in 1986, the USA and Brazil had a reduction in corn production on order of 7% due to the bad weather conditions. The production of rice decreased in the USA and increased about 15‘ in Brazil during 1979-86. The soybeans production in Brazil has been rising since 1980; floods in the south of Brazil in 1986 caused the decrease of soybeans production. While in the United States the production of wheat has remained steady since 1980, in Brazil a rise of about 80‘ occurred during 1985 mainly due to the new produc- tion lands on the center west region of Brazil. Even though the production of grains in Brazil has been rising steadily during the last 30 years (see Figure 1.1), Brazil still imports cereal grains (corn, wheat, rice). Soybeans is a major export grain of I Y r U V f V V run run run run run run if" rim rin:tiu an» Yet Figure 1.1: Main grains production in Brazil from 1950-1986 (Source: EA0, 1987). Brazil. In 1986 Brazil exported 1.2 million tonnes of soybeans and imported 2.2 million tonnes of wheat (FAO, 1987). The major problems with Brazilian agriculture are the lack of government incentives, the lack of cultivated land and the low yield; the corn yield in Brazil is about 1,645 kg/ha compared with to 7,487 kg/ha in the USA (FAO, 1987). Grain is often harvested at moisture contents that are too high to store without spoilage for the selected storage period. Table 1.3 lists the range in the average moisture content at which grains are usually harvested and stored. Different treatments are available to preserve,grains at high moisture contents; drying of grain is the most widely used grain-preservation method (Brooker et a1., 1981). In the grain drying industry, the main objective is to obtain a uniform final product of high quality. A large variation in the inlet moisture content of the grain reaching the dryer usually results in Table 1.3: Maximum and optimum moisture content (% w.b.) for grains at harvest and safe storage. Maximum Optimum Cereal Harvest Harvest 6-12 mo. Over 1 yr. Moisture Moisture Storage Storage Barley 20 18 l4 l3 Edible Beans 20 17 16 14 Corn 30 23 14 13 Rice 28 22 14 13 Oats 20 18 14 13 Wheat 20 18 14 13 Soybeans 18 17 12 11 Sunflower 22 20 10 8 Source: Bakker-Arkema (1988) underdrying and overdrying of part of the grain. Grain stored at a moisture content above the accepted standard is susceptible to spoilage. Overdrying of grain results in the loss of energy, quality and through- put . The manual control of continuous-flow dryers is a difficult task. It is usually applied after observation of the inlet moisture content, the outlet moisture content and the outlet grain temperature by: (1) adjusting the throughput, (2) controlling the inlet air tempera- ture, (3) changing the air-flow rate, or (4) combining (1) through (3). In corn dryers, manual control usually consists of adjusting the throughput. In the rice industry, the operation of multi-stage concurrentflow dryers consists of adjusting the dryer inlet air tempera- tures according to the maximum allowable grain temperature in the tempering zones. The control performance depends basically on the qualification and experience of the operator. Large variations in the inlet grain moisture always result in some overdrying and underdrying. In general, the achieved manual control is only marginal. The dryer operation can be improved by automatic control (Bakker-Arkema, 1984). The process is capable of saving 5-30% in energy compared to manual control systems and results in less underdrying/over- drying and loss of throughput. Automatic control of the drying process has encountered con- siderable difficulties. The two main reasons are: (1) the complexity of the process, and (2) the lack of commercially reliable on-line moisture meters. The recent developments in digital computers, microelectronics, and control theory have contributed greatly to the implementation of control systems. Automatic moisture controllers already are available for single-stage grain dryers. However, the development of controllers for multi-stage dryers is still lacking. The main objective of this study is to design a controller for multi-stages dryers which minimizes the variation in the outlet moisture content at arbitrary inlet moisture content oscillations. Different control strategies will be considered for two different dryer types (the crossflow dryer and the concurrentflow dryer). CHAPTER 2 OBJECTIVES The objectives of this dissertation are: . To develop different linear models for describing the dynamic of the drying process. . To develop several control systems for the control of continuous-flow grain dryers based on system identification and adaptive control. . To test the control systems on commercial crossflow grain dryers. . To develop the unsteady-state model of multi-stage concurrentflow grain drying. . To develop an automatic control system for multi-stage concurrentflow grain dryers. CHAPTER 3 LITERATURE REVIEH Continuous-flow grain drying is a complex process which re- quires expertise to obtain acceptable control performance. Large oscillations in the grain inlet moisture and BCFM content, in the am- bient conditions, static pressure and drying characteristics often affect deleteriously the dryer operation. The design of control systems for continuous-flow dryers re- quires creativity and ingenuity. A major difficulty in the design of a control-system is to reconcile the large-scale, complex, real problem with the simple, well defined problems that control theory considers. It is difficult to study and compare control systems for grain dryers experimentally; a large amount of grain of varying moisture content and accurate instrumentation are required. Computer simulation provides a quicker method of assessing the performances. In this study, a model of a concurrentflow dryer is developed to predict the unsteady- state behavior of this dryer type resulting from varying inputs. The chapter leads of with a review of grain dryer systems. The development of modeling different grain dryers is reviewed in the second part of the chapter. The design and implementation of grain dryer con- trol systems are discussed in the third part. 3.1) W Grain dryers fall into two categories: (1) batch dryers, and (2) continuous-flow dryers. In batch dryers, the grain is dried either with heated air in shallow layers of less than 1 m thickness or with low-temperature air in beds of several meters in depth. The drying may take place in hours, days, weeks or even months. Batch dryers will not be considered further in this thesis. Continuous-flow dryers are classified according to the relative direction of flow of the grain and the air. The four basic types are: (l) crossflow, (2) concurrentflow, (3) counterflow, and (4) mixed-flow. In the crossflow dryer, the drying air passes perpendicular to the direction of grain flow. In the concurrentflow dryer, the air and the grain flow in the same direction. In the counterflow dryer, the air and grain flow in opposite directions. Grain in mixed-flow dryers is dried by a combination of crossflow, concurrentflow and counterflow actions. Figure 3.1 illustrates a schematic of the four types of continuous-flow dryers. The crossflow and concurrentflow dryers are also available as multi-stage units. 3.1.1) We: The main characteristics of the crossflow dryer can be seen in Figure 3.2.a: a) Grain on the air inlet side dries first; by the time it leaves the dryer, some of this grain is overheated and overdried. b) Grain on the air exhaust side is usually underheated and underdried. c) The difference in moisture content between the air inlet and exhaust sides of the grain column makes mixing after drying essential. Crossflow dryers are simple in construction. They generally have lower initial cost than other continuous-flow dryer types. Commercial crossflow dryers are usually non-mixing type dryers. CROSSFLOW CON CURRENTFLOW lean Ooh! Air Ham ‘9 —) :7“! Heist __€>‘* l was: Oman! Ab COUNTERFLOW MIXED-FLOW lei-t ° W I Ibis! Exhaust Air lam 00h! ur _' groin m __) air :3“! Figure 3.1: Schematic of the four basic types of continuous-flow grain dryers . 10 The crossflow dryer is at present the most widely used system in the USA. Figure 3.3 shows a schematic representation of the simple crossflow dryer with a crossflow cooler. This design leads to a energy consumption of 7,000-9,000 kJ/kg (Nellist, 1982). An improvement in the energy efficiency is obtained by recy- cling the cooling air and part of the drying air (Lerew et al.,1972; Meiering and Hoefkes, 1977; Pierce and Thompson, 1982). Reversal of the airflow direction in crossflow dryers is a design used to reduce the moisture differential in the dried grain. Crossflow corn dryers without air-reversal (or a grain inverter) have gradients across the column as large as 20% in moisture content and 50% in grain breakage (Gustafson et a1., 1981). An example of a crossflow dryer with air recirculation and air-reversal (the so-called Hart-Carter design) is illustrated in Figure 3.4. The specification of a typical commercial-size crossflow dryer with air recirculation and air-reversal, and some specific test results of the drying of corn are shown in Table 3.1. Three new features have recently been added to the basic cross- flow design, differential grain-speed, grain mixing and tempering (Moreira, 1983). Tests have shown an improvement of this dryer type in the energy efficiency and grain quality compared to conventional crossflow drying (Bakker-Arkema et a1., 1982). Figure 3.5 shows a schematic of the so-called differential grain-speed crossflow dryer. Table 3.2 shows some specific test results of the drying of corn in a commercial-size crossflow dryer with differential grain speed. 11 a . ' i s I " 3 3 I s . i I .. 3 ’1‘- LAD-Ile- . I 1.5 3: ~- I a“ I a.) I I i l I I '8 i 8 3 Figure 3.2: Moisture and temperature changes during (a) crossflow drying; (b) concurrentflow drying; (c) counterflow drying; and (d) mixed-flow drying. Figure 3.3: Crossflow dryer with forced-air drying and cooling (Brooker, 1981). ‘u ‘ "'1‘ 3 = III" 3 L [ Barn E 1 . a": 2f f Figure 3.4: Schematic of 3-stage crossflow dryer with partial air recycling (Brooker, 1981). 13 Table 3.1: Experimental results of the drying of corn in a crossflow dryer with air recirculation and air-reversal. PARAMETERS VALUE Grain flow rate [tons/hr-m’] 7.8 Grain flow speed [m/hr] 8.0 Inlet moisture content [%w.b.] 29.0 Ambient temperature ['C] 1.0 ['01 8.0 Grain column length [m] first stage 7.6 second stage 5.2 cooling stage 5.5 Cross-section area [m2] 3.2 WEN 200-0 Inlet air temperature [;C] 99.0 Air flow rate [m /min-m ] 15.5 1 971-5 Outlet corn temperature ['C] 16.7 Outlet moisture content [%w.b.] 13.9 Percentage points removed [%w.b.] 15.1 Dryer efficiency [kJ/kg water] 4,536.0 [31 17.5 Source: Rodriguez (1982) Table 3.2: Experimental results of the drying of corn in a crossflow dryer with air recirculation, differential grain speeds and tempering. PARAMETERS VALUE Grain flow rate [tons/hr-m’] burner side 10.7 exhaust side 5.3 Inlet moisture content [tw.b.] 20.5 Ambient temperature ['C] 2.0 ['CI 8.0 Grain column length [m] first stage 3.7 second stage 2.1 cooling stage 0.5 Cross-section area [m’] 1.7 [HP] 60-0 Inlet air temperature [;C] 94.0 Air flow rate [m /min-m ] 9.9 672-6 Outlet corn temperature ['C] --- Outlet moisture content [tw.b.] 15.4 Percentage points removed [§w.b.] 5.1 Dryer efficiency [kJ/kg water] 3,729.0 [11 36,4 Source: Rodriguez (1982) 14 wet grain auger tempering outer F _ / Qrain column_1 " l §__ieated air . Inner grain column 0 variable A speed discharge 1}; cooling air split flow grain discharge ._ Figure 3.5: Schematic of a crossflow dryer with differential grain-speed and tempering. 15 3.1.2) W: The main characteristics of the concurrentflow dryer (see Figure 3.2.b) are: a) The grain and the drying air enter the drying section at the same point; thus the warmest drying air encounters the wettest, coldest grain. b) There is a rapid conversion of sensible heat to latent heat of the water evaporated from the grain; this cools the air down. c) The peak temperature reached by the grain is well below the temperature of the air at the inlet. d) The grain is uniformly dried. Compared with crossflow drying, concurrentflow drying is effi- cient because: 1) the use of high drying air temperature minimizes energy use and the quantity of drying air needed, 2) all the grain receives the same treatment, thus no energy is wasted in overdrying. A concurrent/counterflow dryer consists of one or more concur- rent flow drying stages coupled to a counterflow cooling bed; in the multi-stage units a tempering zone separates two adjoining drying beds (Brook and Bakker-Arkema, 1980). The concurrent/counterflow dryer is a relatively new develop- ment and is at present only manufactured in the U.S.A. Figure 3.6 presents a schematic of a two-stage concurrent/counterflow dryer. The maximum drying temperature in a concurrentflow dryer is not limited by the type or the moisture content of the product; grain velo- city is the determining parameter (Bakker-Arkema, 1984). Air tempera- tures as high as SOO'C have been used in drying corn without affecting product quality (Hall and Anderson, 1980). The energy efficiency of l6 GRAflilN STAGE CMCLMREN WHO ’I______.. tmuwsr ll unrmcnxmc (HUMN OUW Figure 3.6: Schematic of a two-stage concurrentflow grain dryer with counterflow cooler and air recycling. 17 concurrentflow dryers with or without air recirculation ranges from 3,000 to 3,800 kJ/kg (Bakker-Arkema et a1., 1982). The specifications of a typical two-stage commercial-size con- currentflow dryer with counterflow cooler are given in Table 3.3. The operating conditions are for the drying of long-grain rice from 16.6 to 13% w.b. at a rice processing plant. The first drying stage exhibits a fuel efficiency of 5,389 kJ/kg of water removed compared to the second stage (3,177 kJ/kg water). The fuel efficiency of the second stage is affected by the tempering zone between the two drying stages. The mois- ture gradient in the rice is reduced from 5.2 to 0.2 percentage points after 76 minutes in the tempering zone (Fontana et a1., 1982). 3.1.3) W The main characteristics of the counterflow dryer (see Figure 3.2.c) are: a) The grain travels against the flow of the air. b) When this process reaches a steady-state, the grain is exhausting at or near the ambient air temperature, and the air is exhausting at or near the temperature of the warm grain. The process is efficient for cooling but its use for grain drying is limited because of the sensitivity of the grain to high tem- peratures. 3.1.4) W: The main characteristics of the mixed-flow dryer (see Figure 3.2.d) are: a) The air temperature falls rapidly as it penetrates the grain bed. 18 Table 3.3: Experimental results of the drying of long-grain rice in a two-stage concurrentflow dryer. PARAMETERS Grain flow rate [tons/hr-m’] Grain flow speed [m/hr] Inlet moisture content [%w.b.] Ambient temperature ['C] Cross-section area [m2] [101 51-, NH E moon: w oomoobn 'oie oobbbom NH 000:»th N r FIRST STAGE Bed depth [m] Tempering length [m] s 2 Air flow rate [m /min-m ] Inlet air temperature ['0] Outlet rice temperature ['0] Outlet air temperature ['C] Outlet moisture content [8w.b.] Stage efficiency [kJ/kg water] t l SECOND STAGE Bed depth [m] Tempering lengtha[m] Air flow rate [m /min-m ] Inlet air temperature ['C] Outlet rice temperature ['C] Outlet air temperature ['0] Outlet moisture content [tw.b.] Stage efficiency [kJ/kg water] 1 I O H oapol-‘uw NU! Ow NU NH #NHUUDNW uubco H ONWQNN‘O OH O‘DUIWU’UIO‘ UH-I' HM§G¢N COOLER Bed depth [m] s 2 Air flow rate [m /min-m ] Inlet air temperature ['C] -b.l Percentage points removed [%w;b.] Dryer efficiency [kJ/kg water] White rice inlet head yield [t] White rice outlet head yield [t] HNH p U) O\ OO‘@ NO‘O COO Source: Fontana et a1. (1984) 19 b) The grain temperature only rises a few degrees per bed. c) The grain receives a uniform drying treatment. Mixed-flow or cascade dryers are popular in Western Europe and South America. Pollution control is constly in mixed-flow dryers which makes them unpopular in the United States (Hawk et a1. 1978). The inlet air temperature in a mixed-flow dryer can be higher than in crossflow models because the grain is not subjected to the high air temperature for as long a period of time; as a result, 40% less air and energy is needed compared to crossflow dryers (Nellist, 1982). Mixed-flow dryers have the advantage of a concurrentflow dryer without the mechanical complexity. Its disadvantage is that if a low flowrate is used, as when drying very wet grain in one pass, non-uniform moisture is obtained (Hawk et a1., 1978). The energy efficiency of mixed-flow dryers with recirculation air has been reported to be 3,500-4,000 kJ/kg (CNEEMA, 1979). Table 3.4 shows some test results of the drying of soybeans in a commercial-sized mixed-flow dryer. Table 3.4: Experimental results of the drying of soybeans in a mixed- flow dryer. VALUL. Dryer characteristic Effective drying bed length [m] 2.7 W 0.9 Ambient air temperature ['C] 30.6 Ambient humidity ratio [kg/kg] 0.012 Inlet air tempergture ['C] 100.0 Air flow rate [m /min] 378.0 Grain flow rate [tons/hr] 10.1 Inlet moisture content [tw.b.] 18.5 Final moisture content [%w.b.] 16.3 Source: Dalpasquale (1985) 20 r e W 0 b ‘FIW .-.s .I-“n-zs‘asuasx‘ . insulation Ir S=flt exhaust air cooling stage burner .Is.>< a in 5.59.3...533 .....II..m....I...I.._I_. E I) b) C - Cold air exhaust duct. 1 - Aree e! ereeellow. 2 - Area of concurrent-flew. J . Area of cancer-(low. . t u d e. C II. n s. f 1 I t b m I Figure 3.7: a) Schematic of a mixed-flow grain dryer; b) Distribution of air in the ducts of a mixed-flow dryer. 21 3.1.5) W: Different types of dryers other than those included in the preceding discussion have been used to dry cereal grains (Bakker-Arkema et a1., 1978). The most important designs used in the grain industry are: (l) rotary dryers, (2) fluidized-bed dryers, and (3) spouted-bed dryers. A :9;g;y_d;yg; consists of a slightly inclined long cylindrical shell which rotates slowly. In a concurrentflow rotary dryer, the moist grain kernels and the hot drying air are introduced at the same end of the dryer; the dried grain and moist air exit at the other end. Inside of the dryer, lifting flights lift the particle and shower it down in a moving curtain through the air. Figure 3.8 shows a concurrentflow rotary dryer (Keey, 1972). The drying air temperatures in rotary dryers can be as high as 510'C (Ratio, 1974). Rotary dryers are utilized in many rice parboiling-plants for removal of moisture from soaked and steamed rough rice (Bakker-Arkema et a1., 1984). Rotary dryers are expensive to in- stall and require considerable maintenance. Table 3.5 shows typical experimental data for drying parboiled rice in three rotary dryers in series. Parboiled rice is dried in one pass from 35-14t w.b. at an air temperature of 288'C in the first dryer, 232°C in the second, and 149'C in the third unit. Eleven points of moisture are removed in the first dryer, six points in the second, and four in the last unit. The decrease in the fuel efficiency from dryer one to dryers two and three is significant. Eluigizggthgg dryers are used commercially for the drying of milk powder and other fine materials; they also have been tested for drying grains (Pawlowiski, 1975). Figure 3.9 illustrates the design of a 22 Table 3.5: Performance data of three-rotary dryer system in a rice parboiling plant. VALUES Dryer dimensions [m] length 9.8 diameter 2.6 Air temperature ['C] dryer 1 260.0 dryer 2 204.0 dryer 3 149.0 Rice flow rate [ton/hr] 9.4 RPM 10-12 1 90-0 Inlet moisture content [%w.b] dryer 1 34.6 dryer 2 23.3 dryer 3 -17-8 Outlet moisture content [tw.b.] dryer 1 23.3 dryer 2 17.8 dryer 3 14.1 Fuel efficiency [kJ/kg] dryer 1 4,105.0 dryer 2 7,408.0 dryer 3 8,729.0 Source: Bakker-Arkema et al.(1984) typical fluidized-bed dryer. Heated air is blown through an orifice plate (grid) into a bed of particles at a flow rate to cause fluidize- tion. As the particles dry, they lose weight and tend to float toward the product discharge. A proper combination of air velocity and particle velocity is critical for successful operation of a fluidized-bed dryer (Bakker-Arkema et a1., 1978). Advantages of a fluidized-bed drying system are (Pawlowiski, 1975): (l) the excellent contact and thus high heat transfer rate be- tween the particles and the surrounding drying air, (2) the ability to closely control the particle temperature, (3) the uniformity of the drying of the particles, (4) the high thermal efficiency, and (5) the relatively low initial cost. 23 hacydhnes and! -ququu. /5 r5 1 Dryuxoduct Figure 3.8: Concurrentflow rotary dryer (Source: Keey, 1972). 24 Disadvantages of fluidized bed dryers include: (1) the need for a very efficient dust arrestor system, (2) the requirement for a uniform particle size, (3) the high power demand, (4) the difference in fluidiz- ing air velocities for different particles, and (5) the difficulty of switching from one crap to another. Fluidized-bed dryers are not used commercially as grain dryers except for rice in China (Bakker-Arkema, 1988). They are best suited for products which lose moisture primarily during the constant-rate period (Nonhebel and Moss, 1971). Cereal grains, however, dry at the falling- rate period. The range of particles size is another important criterion. If the ratio of the largest to the smallest exceeds 8, the coarse par- ticles tend to settle out while the smallest particles are immediately carried to the dust arrestor (Rearns, 1974). The gngg;gd;hgd dryer, a modification of fluidized-bed, has been tested with different grains (Passes et a1, 1987). A schematic of the spouted-bed dryer is shown in Figure 3.10. The inlet drying air is introduced into the cone-shaped bottom of the bed instead of uniformly over the cross section. The air flows upward through the center of the bed, causing a fountain of particles. The particles then fall into the annulus region near the wall, descending to the base before reentraiment into the central ”spout“. Advantages of a spouted-bed dryer include (Passes et a1., 1987): (1) it can handle particles with a diameter bigger than 1 mm, (2) the intensive particle circulation at low air flow rate, (3) the unifor- mity of the particle drying, (4) the use of high air temperature without particle damage, (5) the low investment cost, and (6) the reduced space for installation. 25 f‘EEZ _. or out cyclone my p oduct out fluidized bed elr heater depenc pla e *— °" '" Figure 3.9: Fluidized-bed dryer. 1 i cut solids dl ent mmf°°m solids streamlines annulus spout at Milan Figure 3.10: Spouted-bed dryer. 26 Disadvantages are: (1) the high pressure drop, (2) the limited capacity per unit space, (3) fluid mechanics controls the air flow rather than heat and mass transfer, and (4) the difficulty to scale up. Speuted-bed dryers are not used widely in the drying industry; most applications are associated with high value, low volume materials. Table 3.6 lists results of a sample design calculation for drying wheat in a spouted-bed dryer (Passos et a1., 1987). The capacity Table 3.6: Performance data of the drying of wheat in a spouted-bed dryer with a crossflow cooler. VALUES Ambient temperature ['C] 18.0 Initial moisture content [%w.b.] 19.0 Wheat flow rate [kg/hr] 840.0 I'Cl 21.0 Bed diameter [m] 0.6 Inlet air nozzle diameter [m] 0.1 Cone angle ['1 90.0 Dryer height [m] 1.2 Fan power [kW] 3.7 Airflow rate [kg/hr] 907.2 Mean residence time [minutes] 17.0 I'Cl 230.0 Outlet moisture content [%w.b.] 14.0 Outlet wheat temperature ['C] 23.0 Percentage points removed [% w.b.] 5.0 Dryer efficiency [kJ/kg water] 4,300.0 Source: Passes et a1. (1987) of this spouted-bed dryer is small, about 1.00 tonne per hour at 5 points removal; the energy efficiency in removing 5 points of moisture from 19.0 to 14.0% moisture content is 4,300 kJ/kg. 27 3.2) W 31-1)an .In thin-layer drying experiments, air at constant humidity, temperature and mass flow rate is passed through a thin-layer of moist material. It was observed in early experiments (Sherwood, 1936) that drying takes place at two distinct rates: (1) at ggng;gn§;zg§g during which the evaporation is limited by external moisture transfer; and (2) at falling;;§§g_nggigg during which the evaporation is limited by internal moisture diffusion. Fer cereal grains, the drying usually takes place in the falling-rate period. This implies that the drying rate of the individual kernels decreases continuously during the course of drying. Prediction of the drying rate of biological products is more complicated during the falling-rate period than during the constant-rate period. External transfer mechanisms (convection and convective mass transfer) and internal transfer mechanisms (conduction and diffusion) have to be considered in the analysis. Many theories have been proposed for predicting the drying behavior of cereal grains in the falling-rate period. They can basically be divided into diffusion and empirical type of relationships (Brooker et a1., 1981). Luikov (1966) described the phenomenon of drying capillary porous products in terms of the following physical mechanisms: (1) liquid transport due to capillary forces (molar transport) and moisture concentration gradients (diffusion); 28 (2) vapor and liquid transport due to moisture and temperature gradients; (3) liquid vapor transport due to total pressure differences. By considering the various fluxes involved in a four-component mixture (four-phase system) of air, vapor, liquid and solid, and using the basic laws of mass and energy transfer, Luikov derived a model of the following form: h_‘vz at {x ........ (3.1) where X" (x,t) - (M,T,p) M - moisture content within the particle T - temperature content within the particle p - total pressure within the particle K.- {K13} - elements which depend on the physical properties of the particle; K11 are phenomenological coefficients and K11, iuj, represent coupling between various transport mechanisms. Although Eqns.(3.1) are widely applicable, they have not been used to describe single kernel grain drying since insufficient data is available for the estimation of the coupling coefficients in the matrix It However, under various simplifying assumptions, modified versions of Eqns.(3.1) have been adapted for the description of grain drying. In the drying of cereal grains, the temperature attained by the grain is sufficiently low to regard the effect of the total pressure gradient term as negligible (Luikov, 1966). Eqns.(3.l) are then reduced to a two-equation system involving only the grain moisture content (M) 29 and the temperature (T). It was concluded that for engineering accuracy, consideration of the coupling effects of temperature and moisture in the analysis of grain drying is not required (Brooker et a1., 1981). Therefore, Eqns.(3.1) reduce to the system: an _ 2 at omv M ...... (3.2.1) d1 _ 2 at otv T ...... (3.2.2) where Dm and Dr represent the moisture and thermal diffusivities, respectively. Since Eqn.(3.2.2) is seldom significant in drying grains (Brooker et a1., 1981), grain drying can be represented by Eqn.(3.2.l): an £38 + an ac - o[ 3:2 g at] ........ (3.3) where D is assumed to be constant. The constant c is zero for a slab, 1 for a cylindrical body, and 2 for a sphere. The following initial and boundary conditions are frequently assumed in solving Eqn.(3.3) (Brooker et a1., 1981): M(r,0) - Min ...... (3.4.1) M(ro,t) - Me ...... (3.4.2) where Min is the initial moisture content and Me is the equilibrium moisture content of the grain kernel. The equilibrium moisture content is defined as the moisture content of the material after it has been exposed to a particular 30 environment for an infinitely long period of time. The Me is dependent upon the humidity and temperature conditions of the environment as well as on the species, variety and hystory of the grain (Brooker et a1. 1981). A number of theoretical and empirical models have been proposed for calculating the moisture equilibria of grains. The theoretical equilibrium moisture content models are based on: (1) capillary conden- sation [Kelvin model], (2) kinetic adsorption [ Langmuir, BET, GAB models], and the field-strength potential [Harkins-Jura model] (Brooker et a1. 1981). The theoretical models are not applicable to grains ever the entire range of relative humidity and temperature values. Therefore, it is preferable to use purely empirical equations until a better under- standing of the physical process involved in moisture equilibria is obtained. A well-known relationship for predicting the Me of grains is the semi-empirical model proposed by Henderson (1952): 1-[Pv/va] - exp [-h*Tab8M1] ...... (3.4.3) where Pv is the water vapor pressure of the grain, va is the saturated water vapor pressure at the equilibrium temperature of the system, M is the moisture equilibrium content (%d.b.) and h and i are product con- stants. Henderson's original Eqn.(3.4.3) has proven to be inadequate for grains (Bakker-Arkema et. al, 1981). Thompson (1967) modified the Eqn.(3.4.3) and proposed the following empirical model of the Me of grains: 31 1-[Pv/va] - exp [-K(T+C)(100*M)N] ...... (3.4.4) where T is the temperature ('C) and the M the moisture content (decimal d.b.); K, N and C are product constants. The empirical Chung equation (Chung and Pfost, 1967) also predicts well the Me values of grain well. The Chung equation has the form: M - E-F ln[-(T+C) ln(Pv/va)] ...... (3.4.5) where M is the moisture equilibrium content (decimal d.b.) and T is the temperature ('C); E and F are product constants. At the present time, the modified Henderson and Chung Me equa- tions are recommended for use in grain-drying calculations. The analytical solution of Eqn.(3.3) for the average moisture content of various regulary shaped bodies can be found in Crank (1957). Pabis and Henderson (1961) made use of the analytical solution of Eqn.(3.3) to describe the drying of shelled corn. They assumed an Arhenius type relation for the moisture diffusivity, D: D - Doexp(’Eo/ROT) ........ (3.5) Chu and Hustrulid (1968) solved Eqn.(3.3) numerically for corn, using an explicit finite-difference method, and assumed the diffusion coefficient to be of the form: D - aoexp(bou) ........ (3.6) 32 Bakker-Arkema and Hall (1965), Young and Whitaker (1971), Rowe and Gunkey (1972), Steffe and Singh (1982), also used the diffusion Eqn.(3.3) to analyze the drying of grains. .Lewis (1921) suggested an empirical model to describe the drying rate, analogous to Newton's law of cooling: fig - -ko(M-Me) ........ (3.7) where k0 is a constant. After integrating, Eqn.(3.7) becomes: MR - exp(-kot) ........ (3.8) where: MR - moisture ratio - g{§lfgf Eqn.(3.8) is often referred to as the exponential (or logarithmic) model. It has been widely used as a basis for modeling the drying rate of grains (Parry, 1985). Page (1949) presented a modification of Eqn.(3.8) for describ- ing the drying of shelled corn. The model has the following form: an - exp(-k'tn) ........ (3.9) where k' and n are drying constants. A number of investigators have used Eqn.(3.9) to describe the thin-layer drying of grains (White et a1., 1973; Misra and Brooker, 1980; Syarief et a1., 1980; and, Huizhen and Morey, 1984). Thompson (1967) proposed the following empirical equation for 33 the drying of shelled corn: 2 t - A01n(IIR) + Boln(MR) ....... (3.10) where t is the drying time in hours, MR is the moisture ratio, and A0 and B0 are empirical coefficients which are functions of temperature. The two-term exponential model of the form: MR - Aoexp(-k1t) + Boexp(-k,t) ....... (3.11) has been used by several researchers (Nellist et a1, 1971; Rowe and Gunkel, 1972; Henderson, 1974; Nellist, 1976) to fit the experimental drying data for different grains. Sharaf-Eldem et a1. (1980) found that the two-term exponential model adequately describes thin-layer drying of shelled corn, rough rice and soybeans. 3.2.1.1) WWW Neither the theoretical nor the empirical drying equations discussed in the previous section represent the drying process of cereal grains accurately over the full moisture range. The reasons why the drying equations based on diffusion theory do not predict the drying behavior of grains accurately are: (1) the improper choice of boundary conditions, and (2) the incorrect assumption that D and k are independent of moisture content (Brooker et a1., 1981). The boundary conditions in Eqn.(3.4.2) imply that the grain surface moisture content reaches the equilibrium moisture content in- stantaneously. This assumption is a simplification. It is more 34 realistic to solve the diffusion equation with a convective type bound- ary condition: D QM a: |1,_r0 - h'd[M(surf)-Me] ....... (3.12) Since the h'd (convective mass-transfer coefficient) is finite, the grain surface moisture does not come to equilibrium instantaneously at the start of the drying process, but comes to equilibrium exponen- tially. Solutions of Eqn.(3.3) with boundary conditions of the type of Eqn.(3.l2) can be found in standard heat-transfer books (Holman, 1984). In the development of the drying equations it has been assumed that the diffusion coefficient (D) or the drying constants (k0, k1, kg, and k') are constant, i.e., they are not dependent on the grain moisture contents. If the drying takes place over a significant moisture content range, this assumption leads to serious errors in the calculated mois- ture contents (Brooker et a1.,l981). Another important factor is the effect of the grain-hybrid and grain-damage on the drying rate of a grain kernel; significant differences in drying rate between different corn hybrids, and between low-level and high-level damaged corn of the same hybrid have been observed (Bakker-Arkema, 1988). Different models for calculating the drying rates of cereal grains have been presented. Eqns.(3.3), (3.8), and (3.9) give satisfac- tory results if D or k-values are known, and the drying takes place over a limited moisture content range. If greater accuracy is required in the predicted drying rates, as in simulation of deep-bed drying, the convec- tive boundary condition of Eqn.(3.l2) and a variable 35 -diffusien coefficient equation may have to be employed in conjunction with the diffusion equation. Finally, the empirical equations such as Eqn.(3.lO) and (3.11) give excellent results within the temperature and moisture range for the particular grain for which they were developed. 3.2-2) W A thin-layer model does not describe the heat, mass and momen- tum transfer processes in deep-beds of grain; it only provides the necessary equation for the drying rate of the particular grain which is dried in the deep bed. Deep-bed models are generally divided in two types: (1) empiri- cal or semi-theoretical, and (2) theoretical. The first type leads to algebraic-type equations; the second to more complex partial differen- tial equations (p.d.e.). The empirical models have contributed significantly to the understanding of the process involved in deep-bed grain drying. However, due to the various assumptions inherent in their derivation, they are less accurate than the theoretical p.d.e. models (Perry, 1985). Thompson et a1. (1968) presented semi-theoretical models for the continuous-flow drying of grain. The models are based on heat and mass balances taken over a thin-layer of grain in which it is assumed that conditions are constant over a given increment in time. Steady- state crossflow, concurrentflow and counterflow drying were developed. Boyce (1966), and Henderson and Henderson (1968) used a similar approach to simulate the drying of a stationary deep-bed of grain. Bakker-Arkema et a1. (1974) presented a more fundamental ap- proach. Based on the laws of simultaneous heat and mass transfer, they 36 developed the steady-state fixed-bed, crossflow, concurrentflow and counterflow models. Sets of three differential equations (p.d.e.), plus an appropriate thin-layer rate equations are employed to describe the drying in various stationary and continuous-flow drying systems. The p.d.e. models for crossflow, concurrentflow, counterflow and fixed-bed are similar in form; however, they are solved using different numerical methods. Laws and Parry (1983) presented the Michigan State University (MSU) p.d.e. models in a general form. O'Callaghan (1971) presented a discretization of the p.d.e. models to simulate continuous-flow grain dryers. Nellist (1974) used the same approach to simulate the drying of a fixed-bed of grains. The drying bed is considered to consist of several thin-layers of grains. Heat and mass transfer equations are solved to calculate the changes in grain and air conditions for every layer for every time step until steady state is reached (Perry, 1985). The model has been successfully used in a number of simulations, including those of concurrentflow, counterflow, and mixed-flow type dryers (Bruce, 1984), and of crossflow dryer (Nellist, 1987). 3.2.2.1) MW The MSU steady-state gxgggflgggngggl‘with the appropriate boundary conditions has the following form (Brooker et a1., 1981): 3.1 _ __-.th_ (T-O) (3 13 1) 6x G‘ca + GacvW h c (T-O) __hLa_ g5 - G c + G c'M (T'O) ' G c : GYc M Ga 8x """ (3'13'2) P P P P P P V 37 as. _ Ends ..... (3.13.3) 6x Ga 8y 3% - a single-kernel drying equation ..... (3.13-4) T(0,y) - T(inlet) 0(x,0) - 0(initial) W(0,y) - W(inlet) M(x,0) - M(initia1) The MSU steady-state ggnggngngflgg_ngggl with the appropriate boundary conditions has the following form (Brooker et a1., 1981): £1 dx - 6.3; G‘cvW ('r-o) ..... (3.14.1) h c (T-O) it + y gfl ('r-0) 6 ..... (3.14.2) dx Gpcp + GpcwM G cp + GpcwM a dx 6 sill _ .2 as ..... (3.14.3) dx a!I dx 3:: - 1;, g; (orig) ..... (3.14.4) - 1 r M - 1, 10M a: ..... (3.14.5) T(O) - T(inlet) 0(0) - 0(initial) W(O) - W(inlet) M(0) - M(initia1) 38 Equations 3.14.4 and 3.14.5 allow calculation of the single- particle drying rate and the moisture content distribution within the particles. The simulation of a tempering in a multi-stage concurrentflow dryer is accomplished by solving Eqn.(3.l4.4) for isothermal and isomoisture conditions over a period of time equal to the traverse-time of the grains through the tempering zone (Bakker-Arkema, 1987). Brook (1977) applied the MSU concurrentflow model to multi- stage concurrentflow corn drying. A diffusion type thin-layer equation was used to describe moisture content distribution inside the kernel in order to model the tempering process. Bakker-Arkema et a1. (1982) used the thin-layer diffusion model developed by Steffe (1979) to evaluate tempering time required in a multi-stage concurrentflow rice dryer. The MSU steady-state gggnggrflgg_ngggl with the appropriate boundary conditions has the following form (Brooker et a1., 1981): $31 .. ' - dx caca + cacvw (T o) ..... (3.15.1) h c (T-0) f}: Gc +60; (T “*FELIGVc'u sag ..... (3.15.2) P P P P P P G R! _ .2 9H ..... (3.15.3) dx G£ dx 3% - a single-kernel drying equation ..... (3-15-4) T(L) - T(inlet) 0(0) - 0(initia1) W(L) - W(inlet) M(O) - M(initial) 39 In addition to a set of differential equations, an expression for the equilibrium moisture isotherm for the particular grain being dried along with a model for the psychrometric chart are combined to form the simulation model of one of the drying systems. Each system of equations describing crossflow, concurrentflow and counterflow grain dryers is solved simultaneously by numerical integration, using finite difference substitution in the derivatives. The crossflow model is solved by standard finite-difference methods. The counterflow model equations, which constitute a two-point boundary system, require application of optimization techniques. The concurrent- flow model can be solved by directly applying standard Runga-Kutta techniques. The basic deep-bed grain-drying models presented in this sec- tion are capable of predicting the steay-state performance of crossflow, concurrentflow and counterflow grain dryers to within 10% of the ex- perimental drying rates and temperatures (O'Callaghan et a1., 1971). Mixed-flow dryers, unlike concurrentflow, crossflow and coun- terflow dryers, are not described by a specific mathematical model. This dryer type can be simulated by alternately using counterflow and concur- rentflow models, instead. This approach has been successfully used by O'Callaghan et a1. (1971) and Bruce (1984). 3.2.2.2)Wm13 Modeling of zg;3;y_gzygrg requires simultaneous solution of a series of equations expressing (l) the heat and mass transfer of the individual particles, and (2) the movement of the particles in the rotary dryer. 40 Sharples et a1. (1964) developed a steady-state rotary dryer model which is very similar to the concurrentflow dryer [see Eqns.(3.14.l - 3.14.5)]. The major difference in the two simulation models is found in the term GP, the particle transport rate through the dryers. In the case of the concurrentflow dryer, Gp is a direct function of the positive displacement of the unload augers; for the rotary dryer, the particle transport is a complicated function of the cascading, bouncing, rolling and airflow encountered by the particles in the dryer (Bakker-Arkema et a1. 1987). The term CD in the rotary dryer is equal to the product of the product density (pp) and the velocity of the particles (VP) along the dryer axis. In turn, Vp is the ratio of the dryer length (L) and the average particle residence-time (Tr) at the dryer. In general, the equation for the residence-time in a rotary dryer is of the following form (Sharples et a1., 1964): L- Tr " c,o N (tan a + c,va) ..... (3.16.1) where L is the dryer length, D the effective inside dryer diameter, N the rotational dryer speed, a the drum slope, Va the air velocity, and 01 and C, are constants depending on the flight design and the material to be dried. In fluidizgg;hgg dryers, as well as in angnggg;hgg dryers, the mass of particles is expanded by the air flow and is vigorously mixed. The particles do not remain in layers as in the packed-bed dryers, but they are considered to move at random. Thus, modeling of fluidized-bed and spouted-bed dryers requires simultaneous solution of 41 the single-particle heat and mass transfer equations, and the residence- time distribution of the particles in the dryer. The term VP' the particle velocity, in a fluidized-bed or spouted-bed is the ratio of the weight of the particles in the bed (w) and the mean residence time (Tr). The residence-time distribution, E(t), in a fluidized-bed dryer or spouted-bed dryer can be expressed as (Vanecek et a1., 1966): -t/T E(t) - (1/Tr)*e ‘ ..... (3.16.2) where t is the time (sec) and TI is the mean residence time of the particles in the bed. Attempts to model fluidized-bed dryers have been made by O'Callaghan et a1. (1971), Pabis (1971), Pabis (1974), and Thorpe Stokes (1987); to simulate spouted-bed dryers by Becker and Sallans (1960), Zuritz and Singh (1982), and Claflin and Fane (1984). 3.3) SEW The literature on the automatic control of grain dryers can be divided into two categories: 1) control of in-bin grain dryers; and 2) control of continuous-flow grain dryers. The basic objective is similar for both types, namely to maximize dryer throughput at optimum energy efficiency and minimum grain-quality deterioration. 42 The control of in-bin dryers consists of controlling the drying fan or/and the dryer heater. In continuous-flow dryers, the rpm of the dryers discharge auger or/and the dryer heater are controlled. .Continuous-flow grain dryers are frequently manually control- led. This procedure often leads te overdrying and stress-craking of part of the grain; it is also labor-intensive because of the half-hourly data-taking requirement (Brooker et a1., 1981). Overdrying of grain is costly because the grain price is usually based on a specific moisture content. Therefore, overdrying leads to the loss in weight of the grain to be sold due to excessive moisture evaporation. Table 3.7 lists the cost of overdrying corn in different years for a 25,416 tonnes (1 million bu) drying facility. One percent overdrying in 1987 resulted in a shrink loss of US$ 15,205. In addition to the loss in weight, overdrying is costly because Table 3.7: Shrinkage in bushel and cost resulting from various levels of overdrying of 25,401.6 tonnes of 15.5% w.b. corn. YEAR OVERDRYING SHRINKAGE 1987 1985 1983 COST PER BU (US$) (81 (bu) 1.32 2.35 3.20 0.25 2,950 3,834 6,932 9,440 0.50 5,882 7,647 13,824 18,824 1.00 11,696 15,205 27,485 37,427 1.50 17,442 22,674 40,988 55,814 2.00 23,121 30,058 54,335 73,988 Source: Bakker-Arkema et a1. (1987) of the extra energy required to dry the grain beyond the moisture 43 content at which it is priced by the market (i.e. 15.5% for corn). The extra energy needed in the drying process, an extra energy cost, is listed in Table 3.8 for different percentages of overdrying. The data show that at 1.0% overdrying requires 2,114 BTU additional per bu, and costs US$ 10,570 per 25,401.6 tonnes assuming the 1987 average U.S. energy cost was US$ 5.00 per lOOBTU. In other years the losses might have been higher or lower depending on the corn price and energy costs during those years. Table 3.8: Energy required per bushel and cost resulting from various levels of overdrying of 25,401.6 tonnes of 15.5% w.b. corn. ENERGY ENERGY COST PER MCF (US$) OVERDRYING REQUIRED J...Q9__5_..99___L.QQ_ (1L (BTU/bu) W 0.25 531 1,593 2,655 3,717 0.50 1,061 3,183 5,305 7,427 1.00 2,114 6,342 10,570 14,798 1.50 3,184 9,552 15,920 22,288 2.00 4,346 13,038 21,730 30,422 Source: Bakker-Arkema et a1. (1987) Underdrying of grain is more serious, since wet spots and spoi- lage may result. If considerable mixing takes place soon after drying, some underdrying is not serious, as moisture equalization will occur. For many years, the automatic control of continuousoflow dryers was limited to temperature/feedback controllers which measure the ex- haust air temperature at several locations along the drying column. As the grain inlet moisture increases, the exhaust air temperature decreases; this change in temperature acts as the input signal to the controller for adjusting the speed of the discharge auger, and thus the 44 grain flow rate. Control of the outlet moisture content based on a change in the air-exhaust temperature has in practice proven to be inaccurate and inconsistent (Palmer, 1984). The main reason for the inaccuracy is the uncertainty of the functional relationship between the air-exhaust temperature and the dryer-outlet moisture content. Now follows a review on the most significant studies on the automatic control of continuous-flow grain dryers. One of the first papers on automatic control of continuous-flow grain dryers was presented by Zachariah and Isaacs (1966). They used the Hukill dying model (1954) to simulate an automatic control system for a crossflow corn dryer. Four control systems were investigated: (1) a proportional-integral-derivative (PID) control, (2) a PID controller with a proportional feedforward from the inlet grain moisture content, (3) an on-off feedback controller and, (4) a combination of on-off and PID controllers. Optimization methods were used to determine the con- troller parameters by minimizing the quadratic error of the dryer-outlet moisture content in response to a step change in the inlet moisture content. The system was not implemented on a commercial dryer due to the lack of on-line computing and moisture sensors at that time. The Zachariah-Isaacs controller is dependent on the working conditions. Simulation results showed that the control system would be very unstable under drying conditions different from the one under which it was optimized. Holtman and Zachariah (1969b) designed the first optimal con- troller for continuous-flow grain dryers. They first investigated the accuracy of a logarithmic and a simple linear models in control of a simulated crossflow grain dryer (1969a). Because of its simplicity, the 45 linear model was preferred and it was used in the follow-up study. The linear model, as described in Holtman and Zachariah (1969a) has the following form: M0(k) - b*t(k) + HI(k) ....... (3.17) where no is the outlet moisture content (decimal d.b.), t is the dryer residence time (hours), MI is the initial moisture content ( decimal d.b.) and b the drying constant. In designing the optimal control sys- tem, Holtman and Zachariah (1969b) used the minimum.integral square error as the performance criterion: N 2 I - Z [H(1)-°] ....... (3.18) 1-1 where W is the setpoint and N is the number of layers in the dryer column. Linear quadratic programming was used to solve the control problem. The control system could not be implemented due to the exces- sive on-line calculation requirements. The Holtman-Zachariah optimal control is an adaptive controller where the value of the drying constant b is updated at each sample interval. Unlike the Zachariah-Isaacs controller, the Holtman-Zachariah control system has the advantage of adjusting its behavior to the change characteristics of the controlled process and its signals. A feedforward control strategy was investigated by Clifford (1978) for a concurrentflow dryer. He developed an unsteady-state dryer model to study different control alternatives. The inlet air temperature was used as the control input instead of the grain flow rate. The 46 Clifford feedforward control system works in this manner: in response to a step change in the inlet grain moisture content, the control parameter (inlet air temperature) is altered according to a predeter- mined pattern. This method is ideal for moving from one steady-state to another. However, it can not cope with continually varying inputs. Olesen (1978) presented an automatic controller for a mixed- flow dryer based on a "weighted-sum" feedforward method. The dryer output rate is adjusted according to a pseudo-moisture content defined as the weighted average of the inlet moisture content values of the grain currently within the dryer. Shift registers are used to memorize the value and position of each initial moisture content as it moves trough the dryer. The Olesen's control requires a feedback loop in the system to check for the output error. The controller has been used on the Cimbria dryers in Denmark, but no published test results are avail- able. Fabian et a1. (1980) designed and implemented an on-off feed- back control system on a mixed-flow corn dryer. A capacitance-type moisture meter, located at the lower part of the drying zone, was used to continuously measure the outlet grain moisture content. The accuracy of the automatic controller is reported to be three times better than the manual control. One of the advantages of an on-off control method is that it can prevent any of the grain leaving the dryer underdried. This method can be considered more a control aid than an automatic control system (Agness and Isaacs, 1967). Hoden and Nybrant (1980) designed an adaptive control system for rotary drum dryers. The control system is a combination of the recursive least square identification with the generalized minimum 47 variance controller (Isermann, 1981). Temperature was used instead of moisture content as the control output due to the lack of reliable moisture meters at that time. The drying process was described by a linear stochastic difference model of the following: A(z'1)*Y(k) - 8(2")*U(k)+D(z-')*V(k)+C(z'1)*E(k)+f ....... (3.19) where Y is the control output, U the control input, 9 is the known disturbance to the process, f describes the working level, 8 is the white noise, and A, B, C and D are polynomials of this form: A - 1+a,z'1+...+anz'“ ..... (3.20.1) a - b,+b,z"+...+bnz'“ ..... (3.20.2) c - l+c1z'1+...+cnz'n ..... (3.20.3) 0 - d,+ d,z'1+...+dnz" ..... (3.20.4) -1 -1 where z is the backward shift-operator, z Y(k)-Y(k-l); r is the control input time delay, 7' is the feedforward delay, and a,...am, b0...bm, c1...cm, and do---dn are the model parameters. The control system was designed based on the minimization of the variance of the quadratic of the control error: I - E([Y(k+l)-W]2+ p[U(k)-Ur(k)]2) ....... (3.21) where p is a penalty factor on the control input and Ur is the input reference. Also, an integral method was included in the control system 48 to avoid offset. The control system was implemented on a commercial rotary drum dryer. A small output variance without offset was experienced with the adaptive controller. A multi-input multi-output feedback control system was developed by Jaaksoo et a1. (1982) for the control of a crossflow grain dryer. Two single input-output linear state variable models were used to describe the drying process: one relating grain flow rate (U,) and grain outlet moisture content (Y1) and, other relating inlet air temperature (0;) and outlet grain temperature. The process model in state-space representation has the following form: X(k+1) - 110:) + 611(k) + d(k) Y(k) - h'X(k) ....... (3.22) where the state I is an n-vector which is formed from measured tempera- tures along the dryer column, the vector d represents uncertainty in the model parameters (EC) and unmeasurable disturbances. An incremental control law of the following form was used: AU(k) - L,Ax, (k)+. . .+LnAxn(k)+Lee(k) ....... (3.23) where AU(k)-U(k) -U(k-1), AX(k)-X(k)-X(k-l), e(k)-Y-€I (the control error), and L1. . ‘Le’ are the control parameters. The controller parameters were determined by minimizing the quadratic criterion [Eqn.(3.20)] with the help of a computer aid design. The control system was implemented with a microprocessor 8085 based controller. It was reported that the accuracy of the control system is between i0.5% of the 49 setpoint. Unlike the adaptive control system developed by Modén and Nybrant (1980), the Jaaksoo control system is of a fixed-type, i.e., the control parameters are determined only once and the control system is designed. To cope with different working conditions (high or low inlet air temperature), two different models had to be developed to describe the dryer operating at low and high temperature. This procedure in- creases the computation and storage requirements for the controller calculations. A microcomputer-based dryer control system (Borsum et a1., 1982) was developed and tested on a pilot-scale, single stage concur- rentflow dryer. The controller is of the feedback type using information regarding outlet grain temperature. The Ziegler-Nichols open-loop tuning method was used to determine the PI controller parameters. Borsum observed that the drying process dynamics are dependent on the discharge rate and then used a sampling interval that is proportional to the grain transportation time in the dryer. Borsum concluded that the calculated controller parameters are dependent on the dryer and grain type. Based on the experimental results, the authors suggested that a feedforward be developed in conjunction with a moisture meter. It was also recommended that for multi-stage CCF dryers different control variables such as, inlet air temperature should be used in each dryer stage. Mann (1982) designed a multi-cascade control system for a rotary sugar dryer. The controller is a combination of feedback and feedforward control. A linear difference.equation was used to describe the dynamics of the drying process. In addition to a cascade controller, the state-space control design was also investigated. Because of its 50 simplicity, the multi-cascade controller was preferred. Computer aid design was used to determine the control parameters. Experimental tests with a commercial rotary dryer showed improved perfomance as compared to manual control. Forbes et a1. (1984) developed a model-based adaptive control strategy for commercial corn crossflow dryers. A microcomputer based control system was designed to automatically control the outlet moisture content. Based on the internal model control technique (Garcia et a1., 1982), the controller was implemented with a PC-type computer. An ex- ponential decay type model was used to describe the process dynamics. The model is of the form: M0(k) - M1(k)*e'b't ....... (3.21.) where MO is the moisture content (%d.b.), MI is the initial moisture content (%d.b.), t is the dryer residence time (sec) and 5 grain drying characteristics (sec'I). The controller input is based on a pseudo- inlet moisture value similar to that proposed by Olesen (1978). Field test results demonstrate that the average outlet moisture content can be kept to within t 1.0% of the setpoint. Forbes' control can be described as a feedforward adaptive control system. It was the first controller to combine the Iweighted- sum' feedforward method with the adaptive approach. The result is a very simple control system. Its accuracy depends on the accuracy of the empirical function which determines the pseudo-moisture content value. An adaptive controller for crossflow wheat dryers has been developed by Nybrant et a1. (1985). The feedback controller is based on 51 the self-tuning regulator method developed by Astrom et a1. (1973); it combines a recursive identification method with the minimum variance control method. A linearization method was employed to determine a linear process model. The microprocessor-based controller is based on the exhaust air temperature, and was tested on a pilot-scale crossflow dryer. It was suggested that a controller based on direct moisture measurements might lead to an improvement of the adaptive dryer control. Nybrant (1986), in a follow-up study, investigated different adaptive controllers for concurrentflow and crossflow grain dryers. Basically, two linear equations were considered in order to model the dynamics of the dryers: a linear stochastic difference model [Eqn.(3.l9)] and a linear model [Eqn.(3.l7)]. Experiments, based on temperature measurements were carried out with laboratory dryers. Simulation studies with direct control of the moisture content are also described. It was found that a feedback/feedforward controller sig- nificantly improves the control quality compared to a feedback controller. A Whitfield (1986) developed an unsteady-state simulation model to study the control of a single-stage concurrent/counterflow grain dryer. The control system is a proportional and integral feedback type. A step-function in the inlet moisture content was used to determine the controller parameters. Simulation results show that the control system is very dependent on the working conditions. It was concluded that a different control system working over a wider range of conditions would be preferred for continuous-flow grain dryers. A microprocessor-based automatic controller was developed and tested on several commercial crossflow dryers (Eltigani et a1., 1986; 52 and Eltigani, 1987). A semi-continuous moisture meter was used to measure the inlet and outlet grain moisture contents. The control system uses a model-based feedforward control algorithm with a feedback loop. Two simple drying process models were used in the control system: an exponential model [Eqn.(3.24)] and a linear model of the form: MO(k) - HI(k)[B,+B,*t] ....... (3.25) where no is the outlet moisture content (decimal w.b.), MI is the in- itial moisture content (decimal w.b.), t is the dryer residence time (hours), and B, and B, are constants. The constants in Eqn.(3.25) were recursively estimated using the least square method. A pseudo inlet- moisture content value is the input and aids in determining the desired grain flow rate. The pseudo-moisture value is calculated from the fol- lowing empirical relationship: Mp8 - a,HI(1)+...+xnhI(n) ....... (3.26) where 51+...+snfl.0, and n is the number of samples used in the calcula- tion of Hp'. The value of ‘1""n were determined by trial-and-error and are kept constant through the course of drying. Since the working condi- tions are different from test to test, a method for estimating the a's values should be incorporated in the software. Tests with commercial crossflow grain dryers resulted in t 0.6% outlet moisture content varia- tion of the setpoint at a variation of the inlet moisture content of 16% to 34% (w.b.). 53 In conclusion, it is clear that automatic control of continuous-flow grain dryers requires microcomputer process-control in conjunction with on-line moisture meters. Because of the large varia- tions in ambient conditions, inlet moisture content and drying characteristics, adaptive controllers have advantages for continuous- flow grain dryers over proportional, PI and PID classical controllers. A simple, but accurate model is required for the adaptive control system design. Also, a feedback/feedforward controller gives significant im- provement in the control quality. 54 CHAPTER 4 The theoretical part of this investigation is divided into two sections. In the first section, the design of the control system for continuous-flow grain dryers is discussed. In the second section, the modeling of the concurrentflow dryer during steady and unsteady state operation is considered. 4.1) W The progress in the development of digital computers and microelectronics has enabled the implementation of complex control algorithms in the grain drying industry. Also, progress in the field of process identification and of control theory has greatly contributed to the development of adaptive controllers. Therefore, interest in adaptive control has increased considerable in the last decade (Isermann, 1981). In this section, adaptive control is evaluated as a tool for continuous-flow grain dryer control. The highly complex dynamics of the dryer provides an ideal test for adaptive control. An adaptive control technique based on a continuously updated linear controller is developed. To design and implement an adaptive control system, three elements are needed: (1) the process model, (2) the control algorithm, and (3) the compensation for offsets. The three elements are investigated below with reference to the control of continuous-flow 55 grain dryers. For detailed information on adaptive control, the reader is referred to Astrom and Uittenmark (1984) and Isermann (1981). 4.1.1) W There are different ways to decrease the grain moisture content in a continuous-flow grain dryer: - by adjusting the throughput - by controlling the air temperature - by changing the air flow rate. Control of corn dryers (concurrentflow and crossflow) is made by adjusting the throughput. No change is usually made to the air flow rate on either corn or rice dryers. For concurrentflow rice dryers, the adjustment is made to the inlet air temperature. In this study, corn dryers are studied. It is assumed that no adjustment is made in the air-temperature or air flow rate during the drying operation. The main physical input to the process of corn drying is the grain flow rate (GFR). The main output is the outlet moisture content. The main disturbance is the change in the grain inlet moisture content (known disturbance). The objective of the modeling of the drying process is to find the dynamic relationships between the described input, output and dis- turbance variables. The partial differential equation grain-drying models are steady-state in nature, and need main-frame capability for on-line calculation (see Chapter 3). Thus, a simple drying non steady-state 56 process model, sufficiently accurate for control purposes, needs to be developed. The adaptive control theory often applies the linear model described by Eqn.(3.l9). Therefore, it is assumed that a continuous-flow drying process can be described by a linear difference model of the following form: A(z-1)*Y(k) - B(z'1)*U(k) + v(k) ..... (4.1.1) where: Y the controlled variable (outlet moisture content) C I the manipulated variable (grain flow rate) v - the disturbance signal k - t/To- the discrete time H I the sample time -1 -1 A(z ) and B(z ) are polynomials of the form: ,1 -1 - A(z ) - l+a1*z +...+an*z ...... (4.1.2) B(z ) - b‘*z +...+b_*z ...... (4.1.3) where m is the model order, 2'1 is the backward shift (or delay) operator: z'1Y(k)-Y(k-1), and a1...a' and b;...bn are parameters. The disturbance signal v(k) can be considered to be one or a combination of the following: (a) a zero-mean unmeasurable disturbance of the form C(z'1)*£(k) where C is a polynomial in 2", and E(k) is an uncorrelated random sequence or white noise; 57 (b) a measurable disturbance 9(k) which can be suitable for feedforward control; (c) a stepwise load-disturbance occurring at a random time: u(k) - v(k-l)+£(k) ....... (4.1.3) (d) a constant offset of the process output, due to a nonlinearity of the process, the actuator, or the sensor. In this study, three forms of combining v(k) and Eqn.(4.l) are considered. 4.1.1.1) Time;§sriss_nsdel_l By considering that the disturbance signal [u(k)] is described by a white noise signal [see category (a) described above], the drying process model [Eqn.(4.l.l)] becomes: A(z'1)*Y(k) - B(z‘1)*U(k) + C(z'1)*£(k) ........ (4.2) where: -1 -1 -1 C(z ) - 1 + c1z +...+cnz E(k) - white noise with zero mean and covariance a”. Eqn.(4.2) is known as the ARHAX (autoregressive moving average) model (Isermann, 1981) because the model is a combination of an autoregressive (AR) part [A(z")*Y(k)], a moving average (MA) part [C(z'1)*£(k)], and a control part [B(z'l)*U(k)]. The parameter terms in Eqn.(4.2) can be considered to represent 58 the drying characteristics for a particular dryer and grain. Variation in the values directly affects the magnitude of the change in the residence time, and thus the control. The variations in inlet moisture content, the ambient condi- tions and other disturbances are accounted for in this drying model by the noise polynomial [C(z'1)*£(k)]. 4.1.1.2) MW By considering that the disturbance signal [v(k)] is described by a measurable signal [see category (b) described above], the drying process model [Eqn.(4.l.l)] becomes: A(z-1)*Y(k) - B(z-!)*U(k) + D(z-1)*V(k-r') ........ (4.3) where: V - measurable disturbance (inlet moisture content) 7' - is the feedforward time delay 1 -1 -m D(z ) - d,*z +...+d‘*z Eqn.(4.3) is similar to Eqn.(4.2) with the exception that the disturbance signal v(k) is considered to be known which allows for feedforward control. 4.1.1.3)1ngum By considering that the disturbance signal [v(k)] is described by a combination of the four disturbances [see categories (a), (b), (c) and (d) described above], the drying process model [Eqn.(4.l.l)] be- comes 3 59 A(z-1)*Y(k) - B(z'1)*U(k) + D(z'!)*V(k-r') + C(z'1)€(k)/A ........ (4.4) -1 where: A - differencing operator (l-z ) Eqn.(4.4) is described in Clarke et a1. (1985) and is known as the CARIMA (controlled autoregressive integrated moving average) model. 4.1.1.4) Ling§;_ugdg1 It is assumed that the drying section of a continuous-flow dryer is divided into n layers (see Figure 4.1). Grain travels as a series of batches, with the batch-speed determined by the discharge rate (GFR). The time [tr(i)] required for a batch of grain, moving as a plug, to pass through a distance equal to the layer depth is defined by: tr“) - EFT-11(7) ...... (4.5.1) and, the dryer residence time (Tr) is equal to: n T - 2 t (i) ...... (4.5.2) r 1_1 r where I is a constant which depends on the dryer characteristics, GFR(i) is the discharge rate, and n is the number of layers in the dryer. The linear dryer model is developed by discretizing the drying section and calculating the residence time for the batches at different levels. 60 GRAIN IN I M g -— ————— —- m g __ _ e E - __ Z s a _e § ._____.3___ fi 4 z 5 3 o __ 2 T- 1 GRAIN OUT Figure 4.1: Identification of dryer segments and grain layers considered in the linear model of the continuous-flow grain drying process. 61 Therefore, by defining the measured output (MO) as a linear combination of the residence time, and incorporating the inlet moisture content as a known disturbance, the drying model can be written as: M0(k) - b*Tr(k-1) + f*MI(k-r') ........ (4.6) where: MO - outlet moisture content correspondenting to the inlet moisture content (% w.b.) Tr MI residence-time of the grain exiting the dryer (hours) inlet moisture content (% w.b.) b,f - parameters 4.1.1.5) W This model was proposed for the design of control systems for grain drying by Merchant (1985): {-b'*Tr(k)] MO(k) - MI(k-r')*e ........ (4.7) where b' is the model parameter. The models described in section 4.1.1 were selected because they are simple and have been used to design control systems for continuous-flow grain dryers. Eqn.(4.2) has successfully described the dynamics of complex processes, such as grain dryers. The main drawback of Eqn.(4.2) is the great number of terms (more than four) needed to adequately represent the process (Nybrant, 1986). A larger model order requires additional computer time and storage for the control parameters 62 calculations. Eqn.(4.3) and Eqn.(4.4) are a better representation of the drying process than Eqn.(4.2) since the models include the measurable disturbance (inlet moisture content). Eqn.(4.4) is still more complete than Eqn.(4.3) because it contains elements of each type of distur- bances. These disturbances may represent: grain inhomogenities, non- linearities in the moisture meter and/or discharge auger, shrinkage and mixing of the grain under drying, etc. Therefore, Eqn.(4.4) is the most realistic representation of the true nature of a grain dryer. Eqn.(4.6) and Eqn.(4.7), although simple, accurately model continuous-flow grain dryers. Their advantage is the small number of terms needed to be estimated for calculating the control parameters. The disadvantage of using the non-linear Eqn.(4.7) to design a control system is that control theory is based on linear systems; thus, the control problem is limited to only one solution. Another limitation of Eqn.(4.7) is that it is specific only for grain moisture content-grain flow rate signals. Other workers have suggested the use of Eqn.(4.2)-Eqn.(4.7) for the modeling of the dynamics of continuous-flow grain dryers (see sec- tion 3.3). However, they have not investigated the general application of such models for both crossflow and concurrentflow grain dryers. This study discusses how these equations can be used to provide accurate control for continuous-flow grain dryers. 4.1.2) W For on-line identification of the unknown process model parameters, recursive estimation (or sequential estimation) methods are 63 suitable. To estimate the parameters in Eqn.(4.2) a FORTRAN subroutine was developed. It performs the recursive prediction error (RPE) method described in Ljung and Sodertrom (1986). The RPE is based on a stochas- tic Gauss-Newton algorithm and can be expressed as follows: The prediction error (e) is equal to: e(k)dY(t)-§(t) ........ (4.8) S(k)-f' (k)P(k-l)$(k)+l(k) ........ (4.9) The gain vector (1) is equal to: 1(k)-P(k-l)i(k)8-1(k) ....... (4.10) e(k)-[a,...anlb,...bn|c,...cn] ....... (4.11) 0(k)-3(k-l)+1(k)e(k) ....... (4.12) P(k)-[P(k-1)-1(k)S(k)1'(k)]/A(k) ....... (4.13) The residual (8) is equal to: E(k)-Y(k)-3,(k)é(k-1)-...-2n(k)é(k-nc) ....... (4.14) d'(k+1)-[-Y(k) ... -Y(k-m‘+l)IU(k) ... U(k-mb+l)|e(k) ... é(k-nc+1)1 ....... (4.15) §(k+1)-3'(k)¢(k+1) ....... (4.15) The filtered signals (Y, U, 3) are equal to: Y(k)-Y(k)-;1(R)Y(k-l)-...-;n(k)Y(k-nc) ....... (4.17) 64 U(k)-U(k)-;1(k)U(k-1)-...-cn(k)U(k-mc) ....... (4.18) E(k)—é(k)-;1(k)3(k-l)-...-cn(k)3(k-mc) ....... (4.19) ¢'(k+1)-[-Y(k) ... -Y(k-ma+l)|U(k) ... U(k-nb+1)|3(k) ... E(k—mc+l)] ....... (4.20) Note: The symbols (') and (‘) in Eqns.(4.6)-(4.20) mean transpose and estimate, respectively. The RPE method is based on the minimization of the loss func- tion due the unknown parameter vector 0 (the estimation of the model parameters): k ___s_’.(.s) _ LF(k) -531 A(k) + ¢'(s)P(s-1)d(s) ....... (4.21) where LF(k) is the loss function and e is the error. The loss function is defined as the sum of the squared prediction errors which here was modified to include uncertainties in the transient phase (Ljung and Sodertrom, 1986), i.e., the use of Eqn.(4.21) allows the estimator to track the time-varying dynamics of the process. In the RPE algorithm used, the matrix P is update using the U-D algorithm given by Thornton and Bierman (1980). The subroutine contains the following steps: (1) Set the initial conditions: at k-O P(I,I)-1; P(I,J)-O 8(O)-0; A(k)-A-O.98 (2) Compute the prediction error: Eqn.(4.19) 65 (3) Update the parameter estimates: Eqn.(4.12) In order to ensure that C(z) contains only zeros inside the unit circle, a stability test is performed in a separate subroutine NSTABL. This routine is based on the Schur-Cohn algorithm [Kucera, (1980)]. (4) Compute the residuals: Eqn.(4.14) (5) Compute the filtered signals: Eqns.(4.17-l9) (6) Update the vectors 4(k) and ¢(k): Eqns.(4.15) and (4.20) (7) Compute the gain vector 1(k), and update P(k) and V: Eqn.(4.10), (4.13), and (4.21), respectively. An extension of the RPE algorithm to Eqn.(4.4) is straighfor- ward. The vectors d,'¢ and O'become: 0(k)-[a1,...,an|b1,...,bnld1,...,d-Ic1...c ....... (4.22) l I d'(k+1)-[-Y(k)...-Y(k-m‘+1)|U(k)...U(k-mb+1)|9(k)...V(k-md+l)|5(k)... 8(k-mc+1)] ....... (4.23) $'(k+l)-[-Y(k)...-?(k-ma+1)IU(k)...U(k-mb+1)|V(k)...V(k-md+1)|3(k)... 3(k-mc+l)] ....... (4.24) To solve Eqn.(4.3), the vectors d,‘$ and O in the RPE algorithm reduce to: e(k)-[a,,....anlb,,...,bn|d,,....dn] ....... (4.25) p'(k+1)-[-Y(k)...-Y(k-ma+1)|U(k)...U(k-mb+1)|9(k)...V(k-md+1)] ....... (4.25) 0' (k+1)-i'(k+1) ....... (4. 27) 66 To solve Eqn.(4.6), the vectors 3, i and O in the RPE algorithm reduce to: O(k)-[b,f] ....... (4.28) $'(k+1)-[Tr(k).MI(k)] ....... (4.29) ¢' (k+1)-v' (k+1) ....... (4. 30) The parameter b' in Eqn.(4.7) is determined directly from the equation and therefore, no parameter estimation is needed. 4.1.3) W The dryer is discretized in n layers as is illustrated in Figure 4.1. The sampling strategy chosen in this study is based on fixed; distance intervals instead of on f1;gd;§1ng intervals. By fixed-time is meant that the time interval between samples is fixed and the number of layers in the dryer varies as a function of the discharge rate. By using the fixed-distance sample strategy, the number of layers are kept fixed and the time interval is variable. The advantage of the fixed-distance strategy is that it allows the determination of a batch of grains at the exact position in the dryer; for instance, the grain outlet moisture content can be exactly matched with the corresponding inlet moisture content. By fixing the time interval between samples, the outlet mois- ture content around the bottom of the dryer flutuate with the magnitude of the error varying with the size of the time increment and the drying rate (Zachariah and Isaacs, 1966). 67 The consequence of the fixed-distance sample strategy is that, at the end of each sample instant k, the following sample interval is calculated: tr(k) - ...... (4.5.3) _L_ GFR(k) 4.1.4) §2n£r21_Alxsxishns A control algorithm for adaptive control should have the fol- lowing properties: - small computation and storage requirement for the parameter calculations; - applicability to several processes types and signals. In the case of grain dryers, a controller should fit different dryers, and must be able to adapt to any variation in the drying process, such as the inlet moisture content, grain characteristics, ambient conditions, etc. Three algorithms are developed for the control of continuous- flow grain dryers in the following sub-sections. 4.1.4.1) GsnsIs1izadaflin1nuI_Xaxian&s_§2nszallsz;19fl!1 The generalized minimum variance control is based on a self- tuner presented by Astrom and Uittenmark (1973). It combines a control law based on linear quadratic criteria with recursive least square identification. The control law is based on the minimization of the linear quadratic criterion: 68 I(k+1) - E[Y’(k+l) + pU2(k)] ....... (4.31) where I is the quadratic criterion, p is a penalty on the control input variance, E is the variance, Y is the control output and U the control input. 4.1.4.1.1) Einimun_Xsrisnee.£esdhask_§9ntrsller Assuming that the drying process is described by Eqn.(4.3), the feedback control which minimizes the quadratic criterion [Eqn.(4.3l)] is (Appendix A presents the derivation of the HV controller): G (z)_ Q_izl_ , Qiz__1 mv Y(z) R(z-1) ....... (4.32) where: va(z) - generalized minimum variance feedback control 0(2) - [C(z") - A(z">1*z 3(2) - z*B(z'1) + (p/b.)*0(z"> By substituing Eqn.(4.32) into Eqn.(4.3) the closed-loop system is: .zniz__l___aaiz__1 Y(2) - 6(2) 1 ....... (4.33) ”A(z ) + 28(2 ) where Y(z) - outlet moisture content and u - p/bl. The value of p can be interpreted as a penalty on the input variance [see Eqn.(4.3)], or as a root locus parameter for the characteristic equation of the closed-loop system: 69 uA(z) + zB(z) - O ....... (4.34) A small value of u results in high input and low output, and a large p in low input and high output. 4.1.4.1.2) u1n1mun.2aI1sn22.222Qf2:!§1§.§2fl£12112t The minimum variance feedforward controller is derived in the same way as the minimum variance feedback controller (see Appendix A). The only difference is that v(k) (the inlet moisture content) is measurable for the feedforward control; as a result instead of a con- trol [U(k)/Y(k)], a feedforward control [U(k)/V(k)] is of primary interest. By considering that the drying process is described by Eqn.(4.3), the feedforward control which minimizes Eqn.(4.3l) is: -1 3.4:). 9.11:4 G (2) - - - ....... (4.35) mvf ( ) R'(z'1) where: vaf(z) - generalized minimum variance feedforward control Q'(2) - [D(z") - A(z")1*zx R~ - z*n221L£1samns_§.entmller;_(£2) The minimum variance controllers presented in section 4.1.4.1, frequently lead to an offset between the measured and the desired value when regulating a process. The insertation of an integrator [see Eqn.(4.38)] solves the problem. Here, a controller is presented where the integration is realized in an alternative way. 72 Compared with the minimum variance controller, the pole place- ment controller is based on the desired characteristic equation of the closed-loop system, and not on the criterion minimization. The pole placement controller was developed by Tuffs and Clarke (1985a) and later modified by Nybrant (1986) to include a feedforward controller. It was derived by assuming that the dryer process is described by Eqn.(4.4). Since the pole placement design is based on polynomial manipulations, solving the control problem using Eqn.(4.4) is complex. An alternative was to use a simpler model, i.e., the linear model [Eqn.(4.6)] which was modified to include the term é/A: MO(k) - b*Tr(k-l) + f*HI(k-r') + 5(k)/A ....... (4.40) Note: Eqn.(4.40) is a simplified version of Eqn.(4.4), the controlled autoregressive ineegzeeee moving average model. From Eqn.(4.5.2) : Tr - tr(1) +...+ tr(i) ...... (4.41.1) or Tr(k) - tr(k) +...+ tr(k-n) ...... (4.41.2) where tr is the residence time of each layer in the dryer (see Figure .1 4.1). Using the shift operator 2 , Eqn.(4.4l.2) becomes: ‘ -j+n Tr(k) - Z - (1 + z- + ... + z )*U(k) ....... (4.42) where n is the number of layers and U is the control input ( tr). By substituing Eqn.(4.42) into Eqn.(4.40) there results: 73 AMO(k) - z-l(bZ)*AU(k) + z-"f*AMI(k) + ((k) ....... (4.43) By assuming that the drying process is described by Eqn.(4.43), and a general integrating control law is defined by: J(z-1)Au(k) + F(z-1)HO(k) - H(z'1)fi(k) + E(z'l)AMI(k) - 0 ....... (4.44) where J, F and H are polynomials, E is a transfer function and 9(k) is -1 the setpoint (Note: the term 2 is omitted for simplicity). The closed- loop can be obtained by substituing Eqn.(4.44) into Eqn.(4.43): [AJ+z'1(bZ)F]HO(k)-z-1{(bZ)HU(k)+[z"'fJ-z'1(bZ)]E)AHI(k)+J£(k) ....... (4.45) Let the desired characteristic equation of the closed-loop be given by the polynomial: .1 L - AJ + z (bZ)F ....... (4.46) where degree J - degree 2 and degree F - 0. Since a unit static gain of the closed-loop is desired, it follows from Eqn.(4.45) and Eqn.(4.46) that: L(l) - bZ(1)H(l) ....... (4.47) A simple choice of H is: 74 'l_L.(.D_ “(2 ) bZ(1) Ideal feedforward is obtained by letting: -f' -1 z fJ - z (bZ)E which gives: E _ zr'+l fl From Eqn.(4.46) it follows that: L(l) - bZ(1)F(l) ....... (4.48) ....... (4.49) ....... (4.50) ....... (4.51) since degree F - 0, Eqn.(4.51) substituted into Eqn.(4.46) gives: The closed-loop system then becomes: H0(k) - z'1§§%%§'w(k-r') + %§(k) where the characteristic equation of the closed-loop system L is assumed to be equal to: L - z + p ....... (4.52) ....... (4.53) ....... (4.54) 75 where 8 is a design variable that determines how close the stable poles are to the process zero at the unit circle. The effect of 8 is the following: - small 8: will give poles that almost cancel the zeros of Z and a fast closed-loop system with large inputs; - large 8: will give poles that are closer to the open-loop poles in z-O. The zeros of 2 will not be cancelled and the system response will be slower with small inputs. Therefore, the pole placement controller is given by: J*AU(k) - H*fi(k) - F*HO(k) - swank-w) ....... (4.55) In summary, the pole placement controller can be viewed in the following way: given the polynomial Z for a particular dryer, specify the desired closed-loop properties by defining L. With the given L and Z polynomials, the parameters b and f can be estimated and the control law can be calculated. 4.1.4.3) W The model-based control is described in Eltigani (1987), and consists of a feedforward model-based type with feedback correction and dynamic compensation. By considering that the drying process can be described by Eqn.(4.7), the controller parameter is calculated using the following equation: b' - {ln[HI(k-r')/HO(k)])/Tr ........ (4.56) 76 The residence time Tr is calculated from the following equa- tion: Tr - (ln[Hps(k)/W]}/b' ....... (4.57) where ups, the pseudo-inlet moisture content is defined by Eqn.(3.26). The values of a,...s1 in Eqn.(3.26) are defined as in Eltigani (1987): 11 xi - 1/[1 + (1222/1)] ....... (4.53) n 41.1 - (2/1)/[1 + (122 2/1)] ....... (4.59) where the subscript i represents the inlet moisture content, and the subscript l the outlet moisture content. The sample strategy employed in the control system described in Eltigani (1987) differs from the one that has been discussed in this study; i.e., in Eltigani's control system, the sample is made at fixed time intervals. In this study, the fixed-distance sample strategy is used with Eqn.(4.57). 4.1.5) Ei1terins_2f_ths_£araseter_flstisatisn Under noisy conditions, the controller parameters vary con- siderably, and sudden disturbances such as jumps, peaks or outliers may change the controller parameters without being desired (Isermann et a1., 1982). To avoid unexpected disturbances, filtering of the parameters estimates, before they are used in the controller parameter 77 calculations, is thus used. It results in a smoothing of the parameter estimates. The filter algorithm is: Of1(k) - a*0f1(k-1) + (l-a)*01(k) ....... (4.60) with O Moisture Content :2] W i a l 5 8 3 ° 3 Figure 5.3: Schematic of the adaptive control system for a crossflow dryer. 99 ooven about 1.01%. In measuring the inlet moisture content, the Shivvers and the Motomco moisture meters show good agreement, i.e., only 2% difference, but 2-3 points lower than the value obtained with the oven method. The error in measuring the inlet moisture content is not as serious as the error in measuring the outlet moisture content because of the ability of the control system to account for the error through the dryer model parameters. An AD/DA interface card is used in conjunction with the microcomputer. It is able to collect data from instruments that measure voltage as input and send voltage as output. The card contains 12 bit analog to digital (A/D) and digital to analog (D/A) conversion with an overall accuracy of 0.1%. The A/D and D/A converters can send or accept a voltage up to 4 volts. The specifications for the data acquisition system components are explained in detail in Eltigani (1987). An incremental Optical encoder measures the discharge auger rpm. The encoder outputs 500 cycles per revolution, and is powered by 5 volt supplied by the microcomputer. The auger rpm is read continuously by a tachometer, and is calculated in terms of residence time (and dryer capacity) by the software of the microcomputer. The desired residence time of the dryer is achieved by sending a voltage to the unload auger. The relationship between the auger rpm and the residence time varies with dryer design. 5.1.3) mm The following parameters are measured by the dryer control system: (1) the grain inlet moisture content 100 (2) the grain outlet moisture content (3) the discharge-auger rpm. The values of the inlet and outlet moisture contents and of the rpm are transmitted intermittently to the microcomputer. The controller equations used in the first part of this study are: Eqn.(4.33), Eqn.(4.36) and Eqn.(4.55). Therefore, the control input (auger rpm or residence time) is obtained by using one of the following three equations: i) For the MV-feedback controller: rpm(k+l) - -[qo*ew(k)+q,*ew(k-l)+...+qnfew(k-m+l)+ r1*rpm(k)+r2*rpm(k-l)+...+rm*rpm(k-m+1)] ........ (5.1) ii) For the MV-feedback/feedforward controller: rpm(k+l) - '[qo*ew(k)+q1*ew(k-l)+...+qnfew(k-m+1)+ do*Ami(k-r')+d1*Ami(k-r'-l)+...+du*Ami(k-m-r'+l)+ r1*rpm(k)+r,*rpm(k-l)+...+rn*rpm(k-m+l)] ........ (5.2) iii) For the PP-controller: - * - 'k - tr(k+l) - 1+5 ...... (5.3.1) J - {Tr(k-1) - Tr(k)*[L(1)/Z(1)]) ...... (5.3.2) lOl Eqns. (5.1) and (5.2) are obtained by substituting the control- ler parameters (Q and R) into Eqn.(4.33) and Eqn.(4.36), respectively. Eqns.(5.3) are obtained by replacing the controller parameters L, 2, E, H, and J (defined in section 4.1) into Eqn.(4.55). In implementing the control system, the first attempt was to use the direct value of the measured discharge auger rpm as a control input [see Eqns.(5.l) and (5.2)]. In Eqn.(5.3) the discharge auger rpm is used indirectly, since the residence time tr is inversely propor- tional to the rpm. The residence time of the grain in the dryer is achieved by sending a voltage, corresponding to the specific residence time, to the discharge auger. The relationships between the residence time and the auger rpm, the auger rpm and voltage for the Meyer-Morton 850 dryer were determined experimentally: _ 1229...}. Tr RPM ........ (5.4) RPM - 12%” ........ (5.5) r Voltage - 0.5653 + 0.002543*RPM ........ (5.6) The linear regression method was used to determine Eqns.(5.4)- (5.6) by fitting the experimental data to the predicted curves. In Appendix B the experimental data for the Meyer-Horton crossflow dryer is presented, and the method used to determine Eqn.(5.4) is explained in detail. 102 The sample strategy used in this study (see Section 4.1.3) requires a moisture meter which is capable of sending the measured data every time it is required by the microcomputer. However, the Shivvers moisture meter only measures the moisture content data approximately every 6 minutes. One way of overcoming this problem, and still be capable to use the fixed-distance sample strategy, was to limit the minimum sample time to 6 minutes, i.e., to limit the minimum interval of time between two samples to 6 minutes. This value is obtained by deter- mining the maximum allowed auger rpm for the dryer. The expression for the sample time is obtained by dividing Eqn.(5.4) by the number of layers in the dryer. Therefore, the sample time for the Meyer-Morton 850 dryer is equal to: W-m tr - RPM RPM ........ (5.7) where tr is in hour and the number of layers (n) in the dryer is 10. For the Meyer-Morton, the maximum discharge auger speed value is 1200 rpm. The relationships between the residence time and the auger rpm, and the auger rpm and voltage for the Zimmerman ATP 5000 dryer are: 7200. r ' 7.95*RPM-6390. °°°°°°° (5'3) 6390.*Tr+7200. RPM - 7.95 ........ (5.9) 103 Voltage - 0.0097*RPM°°7943 ....... (5.10) The sample time is equal to: t _ 117200./n _ 600. (5 11) r 7.95*RPM-6390. 7.95*RPH-6390. °°°°°° ' with nr12 layers. For the Zimmerman dryer, the maximum allowed discharge auger speed was 1800 rpm. The voltage to be send to the SCR is converted to its digital equivalent by Eqn.(5.12), and then input to the D/A converter which sends it to the SCR in the dryer controller. The SCR then adjusts the auger rpm accordingly (Eltigani, 1987): VT - Volt*(2047.)/4 ....... (5.12) where: Volt - analog voltage VT - digital equivalent Volt The following procedure was followed in conducting the control- ler tests: (1) the dryer is manually started for a period of time equal to the residence time equivalent to the initial rpm. During this period, moisture content and rpm data are continuously collected by the computer to be used by the control system during subsequent automatic control; 104 (2) after the start-up period has ended, the control system is switched to automatic (the length of a test varied from 5-8 hours); (3) at the end of each test the data are analyzed. 5.2) W Like in a crossflow dryer, the drying time in a concurrentflow dryer is determined by the rate at which the grain is discharged from the dryer. Feed-roll augers are used to regulate and control the grain flow. In multi-stage dryers, the discharge auger is located at the outlet of the last stage and thus the grain flow rate is the same throughout the dryer. Therefore, the same control strategy used to design the control system for a crossflow dryer is considered in the design of the two- stage CCF corn dryer control system. The discharge rate (GFR) is the input to the process, the grain outlet moisture content is the output, and the grain inlet moisture content is the main disturbance. Neither the inlet air temperature nor the air flow rate is adjusted in the two dryer stages during the course of drying. One of the objectives of this study in egeeme;1e_eene;el_efi_ eeneineeeeefleg_g;ein_eryere is to develop a control system which can be employed in both dryer types (crossflow and concurrentflow). Because the grain velocity is the same throughout a two-stage CCF dryer, the control system for this dryer type can be designed by considering the dryer as a one-stage drying process. The main goal is to demonstrate that a two- stage CCF dryer can be modeled as a one-stage dryer using a simple linear model. 105 The following is the description of the two-stage CCF corn dryer used in the simulation study. 5.2.1) W The two-stage Blount/ccd CCF dryer consists of two concur- rentflow drying beds and a counterflow cooler. Between the first and the second drying stages, the grain flows through a tempering or steeping zone. The dryer is schematically shown in Figure 5.4. In Table 5.4 the specifications of the dryer are presented. The dryer is 12.83 meters in height. The length of the first and second drying stages is 0.76 meters. The tempering zone is 5.18 meters in height, and the cooling section measures 1.5 meters. The dryer cross-section area is 9.0 meters. The rated capacity is 34.0 tonnes of wet corn per hour at 5 points moisture removal. 5.2.2) from The same adaptive control system as shown in Figure 5.3 and described in Section 5.1.1 is considered for the concurrentflow dryer. The following parameters are employed in the two-stage concur- rentflow dryer control system: (1) the grain inlet moisture content (2) the grain outlet moisture content (3) the discharge auger rpm. In the second part of this study, the residence time is con- sidered as the control input [U(k)] instead of the rpm [see Eqns. (4.2), (4.3) and (4.4)]. This procedure results in a linearization of the drying process (Nybrant and Regner, 1985). The following is a 106 wet grain exhaust air E-Q-Q OI OI . ist-sta e tempering section tiring air (3 (1 «me— cl cl cl ol :6. ~ cooling section . 2nd-stoge ._ I I I I drying air dry 9min FEW , , recycled exhaust air ambient air II M I I I I I ambient air 0 Figure 5.4: Schematic of a two-stage CCF dryer. 107 Table 5.3: Blount/cdd two-stage CCF dryer specifications. m VALUE. .Airflow rate, 15; drying EESELQD 42,2 [m/min] 4 cooling section 42.7 Static Pressure. Winn—2.1m [Pa] 2nd drying section 2100.0 Grain flow rate, at 5 points moisture 12.4 [m/hr] removal Drying Temperature, recommended 232.2 ['C] Dryer Dimensions [m] lst drying section 0.76 2nd drying section 0.76 cooling section 1.5 tempering 5.2 Dryer Cross Sectional Area, 9.0 [Hz] Rated Capacity, 20%-15% HG 34.0 [tonne/hr] Retention Time, 1.2 [hr] Fuel Type, natural gas 108 detailed description of the linearization method. The output of a continuous-flow grain dryer (moisture content) is approximately a linear function of the grain residence time Tr in the drying section [for example, the linear Eqn.(4.6)]. For a constant discharge rate, the residence time of the grain in the dryer is: 11 r GFR ....... (5.13) where I, is a constant depending on the same factors as 1 [see Eqn. (4.5.1)]. Thus, if the GFR (i.e., rpm) is directly used as the control input, a linear system can not be expected. However, if 12 GFR U - ....... (5.14) is regarded as input, the dryer model can be linearized (Nybrant, 1986). When the control input U is used together with the sampling method [Eqn.(4.5.3)], 11-1 and the sample interval tr will be equal to the control input U. The two linearizations represented by Eqn.(4.5.3) and Eqn.(5.14) are employed for the automatic control design of a two-stage CCF dryer; this means that the sampling is performed with respect to the grain displacement in the dryer, and with the control input equal to the sample interval measured in time. The controller equations in the automatic control of a two- stage CCF dryer are: Eqn.(4.32), Eqn.(4.35), Eqn.(4.36), Eqn.(4.55), and 109 Eqn.(4.57). Therefore, the control input (residence time) is obtained by using one of the following five equations: 1) For the MV—feedback controller: tr(k+l) ' '[qo*ew(k)+q1*ew(k-l)+...+qnfew(k-m+l)+ r1*tr(k)+r,*tr(k-1)+...+rnftr(k-m+l)] ....... (5.15) ii) For the MV-feedforward controller: tr(k+l) - -[qo*AMI(k)+q1*AMI(k-d'-l)+...+qanHI(k~d'+l)+ r1*tr(k)+r2*tr(k-l)+...+rn*tr(k-m+l)] ....... (5.16) iii) For the HV-feedback/feeforward controller: tr(k+l) - -[qo*ew(k)+q,*ew(k-l)+...+qu*ew(k-m+l)+ do*AMI(k-d')+d1*AMI(k-d'-1)+...+dn*AMI(k-m+l)+ r1*tr(k)+r,*tr(k-1)+...+r'ftr(k-m+l)] ....... (5.17) iv) For the PP-controller: tr(k+l) - ..... (5.18.1) 1+5 J - (Tr(k-1) - Tr(k)*[L(1)/Z(l)]) ..... (5.18.2) 110 v) For the MB-controller: Tr(k+l) - [ln(Mps(k)/W)]/b' ....... (5.19) with, Hps(k) - a, *MI(k)+x2 *MI(k.+1)+...+a1 (k+i) ....... (5.20) and s1...s1 as defined by Eqns.(4.58) and (4.59) and b' by Eqn.(4.56). Eqn.(5.15) and Eqn.(5.17) are obtained by replacing the con- troller variables Q and R into Eqns.(4.32) and (4.36), respectively; Eqn.(5.16) by replacing the controller variables 0' and R" into Eqn.(4.33); Eqn.(5.18) by replacing the controller variables L, 2, E, H and J into Eqn.(4.55) and, Eqn.(5.19) by replacing the controller vari- able b' into eqn.(4.57). The values of the resident time and the auger rpm for a two- stage CCF dryer were obtained from a commercial CCF dryer brochure (Blount Inc., Montgomery, AL). The relationship between the residence time and the auger rpm was determined by linear curve-fitting, and was found to be: 1700. Tr ' 12.49+46.4*RPM °°°°°° (5'21) 1700.-12.4mmr RPM - 46.4 ....... (5.22) For the control study of a two-stage CCF dryer, it was assumed 111 that the moisture meter can send the input data to the microcomputer each minute instead of each 6 minutes. This procedure decreases the computer time for the simulation. The sample time was found to be equal to: 1700./n tr ' 12.49+46.4*RPH °°°°°°° (5'23) with n923 layers. For the two-stage CCF dryer, the maximum allowed discharge auger speed is 48 rpm. 5-3) W Experimental data obtained with the Meyer-Horton and the Zimmerman crossflow dryers were used to test the empirical models, i.e., Eqns.(4.2) and (4.4), and Eqn.(4.6), respectively. Simulation results obtained with the partial differential equations model (CCF dryer) provided data to test the suitability of the empirical models [Eqns(4.2), (4.3), (4.4), (4.6) and (4.7)] in describing the dynamics of the drying process. A statistical test was employed to determine the model orders. For example, for Eqn.(4.2), to test if the model is of first order, the following hypothesis is considered: 0 0 0 1'10 ‘ (82 - b1 - C2 - 0) ....... (5.24) By assuming that the asymptotic theory can be applied, the 112 statistic (Astrom, 1970): LF-LF 1 2 *-N—'5— ....... (5.25) 9' LP, 3 has a F1_a(3,N-6) distribution under the null hypothesis [Eqn.(5.24)]. The symbol LF, denotes the minimal value of the loss function for the first-order model, LF2, the minimal value for the second-order model, and N the number of input-output pairs. In using the statistic 6, the hypothesis (5.24) is tested at the a level of significance by comparing 0 with the critical value F1_a(3,N-6). If this critical value is exceeded, the hypothesis that the model is first-order is rejected. See Neter and Wasserman (1974) for an F table. In summary, the implementation of the control algorithms [Eqns.(4.32), (4.33), (4.36), (4.55) and, (4.57)] to continuous-flow grain dryers has been presented. The calculation of the sample time, i.e., Eqn.(4.5.3), has been treated in detail. For the implementation of the GMV controller it was suggested that the residence time (Tr) be used as the control input instead of the rpm because this procedure leads to a linearization of the drying process. For the numerical identification of the drying process, a method for the selection of the order of the model (4.2) has been presented. The basic approach is to compare the performance (loss 113 function) of the model of first and second order, and to test if the higher-order model is required. 114 CHAPTER 6 RESULTS AND DISCUSSION The experimental results of the automatic control of the two crossflow dryers and the simulation results of a two-stage CCF dryer are presented and analysed in this chapter. In the first part, the empirical models are verified and their suitability assessed to describe the dynamics of the crossflow drying process; then, the experimental control data obtained with the Meyer-Morton 850 and the Zimmerman ATP 5000 crossflow dryers are presented. In the second part, the unsteady-state model is compared to the steady-state CCF dryer model; then, the empiri- cal models are verified and their suitability determined to simulate the dynamics of the CCF drying process. Finally, the automatic control simulation results are presented, and the control behavior of the con- trol system is evaluated based on several performance measures. 6.1) W 6.1.1) MW The dryer model is determined directly from measurements (inlet-outlet moisture contents, rpm) on the drying process. In general, the control variable (rpm) is perturbed and the resulting variations in the output (outlet moisture content) are observed. On the basis of the recorded rpm-outlet and/or inlet moisture content pairs, a model of the process and the disturbances is determined. In this particular case, the identification experiments could not be performed with the commercial 115 dryers due to economical reasons. Instead, experimental data obtained during a normal operation test were used. The selected tests were chosen based on the inlet moisture content, grain flow rate and outlet moisture content variations. It is assumed that the length of the drying tests is sufficient to give the necessary information about the dynamics of the process. The experimental data obtained with the crossflow dryers in 1986 were used to test the empirical models [Eqns.(4.2), (4.4) and (4.6)]. The recursive predicted error program (section 4.2.1) was adapted for off-line study. The objective of the first part of this section is to test if the empirical models used in the MV-feedback and MV-feedback/feedforward and PP controllers are suitable for on-line calculations. 6.1.1.1) WW Results of more than 10 hours run with the Meyer-Horton crossflow dryer (Eltigani, 1987) were employed to estimate the parameters of Eqn.(4.2) and Eqn.(4.4). Figure 6.1 shows the experimental data. The results are shown in Table 6.1. To test the hypothesis that model I is of the first order (see Section 5.3), it is assumed that the the asymptotic theory can be ap- plied (Astrom, 1970). The null hypothesis is: 0 0 0 Ho: (82 -b1 "C2 -0) In this particular case, 0 - 1.07. At risk level of 5%, Fo.,5(3,64) is 116 1 500.0 1 1300.04 L L 1100.0-I J QCELO-I 1 1 1.511 700.0 - Discharge Auger RPM 1 l WOO r r fir r V I f 35.00 m—e Inlet “C 25.00 20.00 Moisture Content (Xw.b.) 100m r T f fi r V l’ U I f r f r T r I r 181522 29 38 435057 85 71 Sample Number 0.50 1.32 r 2.04 ' 3.581 4.08 r 8.10 1 8.12 r 7.14 f 8.18 . 0.18 ' 101.20 Time (hr) Figure 6.1: Meyer-Horton experimental data employed to obtain the parameters of model I and model II-b (10/29/86). 117 Table 6.1: Parameters values for the models I and II-b of the Meyer- Morton dryer. eanEL nanansrsns MODEL I MODEL II-b 1st;arder_______2nd;ardsr a, - -0.99:0.01 -1.4li0.06 -0.80i0.06 a, - 0.42:0.07 b, - 0.00026i0.001 0.0020:0.0002 0.0015:0.002 b2 - 0.00061i0.001 c1 - -0.39:0.09 -0.67i0.01 0.088i0.08 c2 - -0.12:0.07 d1 - -0.25:0.5 11388 menus 54.50 51.89 58.02 118 2.76, and the null hypothesis (i.e. that the system is first order) has to be accepted. Figure 6.2 illustrates the identification of the first-order model I. The estimated values show how well the observed outlet moisture contents can be predicted by the model. The identification procedure was based on the assumption that the residuals [mo(t)-mo(t)] are normal and uncorrelated. As Figure 6.2 shows, these assumptions are not violated. Figure 6.3 shows the outlet moisture contents predicted by the second-order model 1. Predicted and observed output moistures are in good agreement. The residuals do not show any violation of the assumed assumptions. Figure 6.4 shows a plot of the outlet moisture contents predicted by the lst-order model II-b. The outlet moisture contents predicted by the model agree well with the observed data. The residuals plot does not show a violation of the assumptions. 6.1.1.2) WWW Experimental results obtained with the Zimmerman dryer (Etigani, 1987) were used to analyze the linear model [Eqn.(4.6)] in describing the dynamics of the drying process. The identifications is based on 130 pair of input-output data. Figure 6.5 shows the experi- mental data. The results of the identification are summarized below: b - -0.03110.007 Loss Function - 50.27 f - 0.93:0.03 119 300 d u a O -i 1 o q 4 0° .1 O :I 1001 o d° o °o o o dd’ o 0e: °’o o ° do 0 o - 53 :JEEhEQ °‘° ° ._. ° ufloJL---3, o ,a___s: g . . . ° . - -* o O o O 0 -l O .1 o O O o 1 do 0 ‘l l o 7 -3.” T r r fit 1 fr f I—T r rfi—T r r r e I T t r r 3500 Q scanner-om a mum: : 'l -— m u 25 3000 malllsfflc .: E J c, 2300 .2 In K E 20.00 (5 2 lg 18.00 ‘Oomfifrrffi'frrrtrrfftrre 1rrr 0. 14.00 28.00 42. 58300 70300 Figure 6.2: Identification results with the first-order model I for the drying of corn in the Meyer-Morton 850 dryer. 120 3.“ 1 -1 J O - : . . ‘ O .. 1.00-1 ° ° 0 ° 0 ° 5+ 9 o 0 ° 010 o d9- 4 010 ° 0 ° ° °°18 - Q 0 a -l "l O O a O O 00 m ‘ O O .1 o O 0 91° 0 O o o O -I 1 o -I 4 «I -3.” 1' Y r firf r T V—r r I r t r r r 1' 1' FY f U r JSJXB IINIE.IZND-OIDCR o lfiflnflfllb -- 0m 3000 mallltrlc 25$!) ZOJXI _ - 98 o a 18.00 ° -, 9 0" A. ° N. .9 o " ° ‘08mfi r r— t r I r r fi v I f 1" r r I r t r r t r r 0.00 14.00 28.00 42.00 8850 701.00 lSHfiIES Figure 6.3: Identification results with the second-order model I for the drying of corn in the Meyer-Morton 850 dryer. 121 £100 1 . o o -l 1 1 1 ° . . 1 1.00-i O o o o 0 .— o a °"\-‘ f.- ...”: o“/--'re‘,-°' ‘\.J 9"... “V“. -./-J ..... l ‘9 I. \.-,‘.e .....1'1 .... t";; \....i T 1‘ a- I. a-Jrv v I ’\S n ‘T . F“— 1 5.00-1 -7‘- \-’~a""‘",\_l\’ \ "‘7’ \ \‘J ‘7} ‘w’ve ,l"‘J L9~I~ \V” j -l b 1 0.00 — .3 .1 .1 5-00" lnlet MC '2 ‘ --- 0utlet MC 1 14 27 40 53 66 79 92 105 118 131 Sample Number [T T r T T T T I T T7 T r T T T I T rTT " 0.00 1.01 2.02 3.04 4.05 5.06 6.07 7.08 8.10 9.1 1 10.12 Time (hr) Figure 6.37: Simulation of the automatic control of a two-stage CCF dryer “81118 W (868 Table 4-1 for dryer parameters) . Discharge Auger RPM Molsture Content (Xw.b.) 180 1 O 00 r I T IT T I T I r T‘ r l r I T T y T r— 30.00 - — eetpolnt: 17.0 MCavg:16.0 .. 25e00" q WM :1 ...-... _,..J .. .. . 15.0033' ~-. 7’“ wa'vw "“~~..'~ ....rA-I ~.‘ " fibl I‘v‘N—J "1 10.00- I 1 1 530: --~ lnlet uc n --- Outlet 110 0.00 T , . r . , . r r r . , . , . , . r . 1 1 4 27 41 54 67 80 93 107 120 Sample Number T I l— T IT T UT T T [T l T I I 0.00 0.66 1.72 2.36 3.44 4.50 6.16 6.02 6.66 7.34 360 Time (hr) Figure 6.38: Simulation of the automatic control of a two-stage CCF dryer using fln;ggntzgllgz (see Table 4.1 for dryer parameters). 181 Table 6.13: Characteristic values of the different control performances with the inlet moisture content variation from Setl and setpoint equal to 17$ w.b. (N - 131). PERFORMANCE CQEIBQLLEB_ NC HEASURES PP1 MV MB fdb2 fdf2 fdb+fdf’ Se(tvxb.) 1.2 1.4 2.7 1.6 1.4 ~- HDavg(§) 17.2 16.3 15.3 16.3 16.0 18.5 MOmin(%) 14.0 13.5 12.1 13.4 14.1 15.0 M0max(§) 19.9 18.8 18.5 19.9 19.0 21.0 MImin(%) 18.0 18.0 18.0 18.0 18.0 18.0 Mlavg(§) 20.4 20.4 20.4 20.4 20.4 20.4 MImax(§) 23.0 23.0 23.0 23.0 23.0 23.0 MIstd(t) 1.3 1.3 1.3 1.3 1.3 1.3 RPMmin 19.0 17.0 16.0 13.0 16.0 -- RPMavg 35.4 26.6 20.6 27.5 25.7 ~- RPMmax , 48.0 48.0 31.0 48.0 48.0 -- RPMstd 10.8 7.3 7.3 8.3 7.2 -- 1 for 5 equal to 50. 2 for p equal to 0.01 3 for p equal to 0.05 where: fdb - feedback fdf - feedforward PP - pole placement controller NV - minimum variance controller MB - model-based controller NC - no control (see Figure 6.28) Se - see Eqn.(6.l) N - number of samples (see Table 6.12) 182 close to the desired value. However, the results obtained with the MB- controller were better than with the HV-feedforward. For the above reasons, the PP and the MV-feedback/feedforward controllers are preferred over the MV-feedforward, MV-feedback and MB controller, and are used in the following simulation study. 6.2.2.2) W To simulate the dryer operation with more realistic inputs, two sets of data (Set2 and Set3 in Table 6.11) were used. They are based on variations in the inlet moisture content observed during a practical farm drying test. In Set2, the inlet moisture content varies widely during the first two hours and remains fairly constant over the last 4 hours. The grain inlet moisture content in Set3 fluctuates at random during the entire drying period. These inputs were simulated without control, and with MV- feedforward/feedback and PP controllers. For simplicity, the MV-feedback /feedforward will be referred to as MV in this section. The results are shown in Figures 6.39 through 6.44. The details of the control performance are tabulated in Table 6.14. Figures 6.39 to 6.41 present the simulation results using inlet moisture variation from Set2. The inlet moisture content has an average of 20.7t, a minimum of 17$ and a maximum of 25.6%. In Figure 6.39, the outlet moisture is shown when no control is applied to the dryer. The MOavg is 18.16 for a setpoint of 16‘. Figure 6.40 shows the results obtained with the PP-controller. The average outlet moisture content is only 0.16 from the setpoint and the control error is 1.93. The large value of the control error is due 183 to large fluctuation in the inlet moisture content during the first 40 samples. The discharge auger rpm is changed frequently in an effort to control the outlet moisture content as close to the setpoint as possible. As a result, part of the grain is overdried and part underdried. However, the result is better than for the uncontrolled case. The level of the control obtained is excellent taking into account the large and sudden variation in the inlet moisture content during the first two hours of drying. The result obtained with the HV-feedback/feedforward controller is illustrated in Figure 6.41. Compared with the previbus results (Figure 6.40), the MV-controller gives a smaller Se (1.56) value and an average outlet moisture content 0.66 point below the setpoint of 166. The 0.66 overdrying is a direct result of the large and rapid changes in the inlet moisture content. It is observed that with the MV-controller the variation of the outlet moisture content around the setpoint is reduced. However, in contrast with the PP-controller, the MV-controller tends to produce overdried grain. In Figure 6.41 it is noticed that at the end of the run and after the first 22 samples, the grain is overdried. The simulation results using inlet moisture content variation from Set3 are shown in Figures 6.42 to 6.44. Table 6.14 list the results of the performance measures. Figure 6.42 shows the results when no control is used. The grain is overdried, the average outlet moisture content is 18.16 for a setpoint of 166 w.b. Figure 6.43 and 6.44 show the simulation results obtained with 184 60.00 2 1 ‘ g 46.00- a s ‘ ' c» 36.00 _ . 1f 1 O u 9 24.004 2 J 1 g 12.00- .. o 1 - o 00 V I U I # T ‘I r I T T I V l U I l I 1 30.00 A J .6 1 g 25.00- ,1. " 0 r , I .. 5 1" ‘I ‘3. '."J' ... .0... '0‘. ’e‘L‘ "'fi."‘ . .. '\ ”--..'o\'o“.-~ ,.....,.. .. (a. ‘5 20.00-j 1.: «.v -.‘ #15:” L. 1 f\;_,~;;j_533......__,.~;_,---;,\;:,. '1 o :1 ‘5; 15.0041" “ o ‘ ‘ 2 1 0.00 " .4 2 ‘ ‘ «3 500" --- lnlet uc . 1 ‘ -- 0 flat MC 0000 T I" I I t T I I U I W I V r Y r I r I 1 12 23 34 45 56 67 78 89 100 Sample Number V ' I U V V r ‘ I t I j I 0.00 0.56 1.16 1.54 2.32 2.00 3.46 4.06 Time (hr) I V r I j 4.64 5.22 5.60 Figure 6.39: Simulation of the automatic control of a two-stage CCF dryer (no control, Set2) (see Table 4.1 for dryer parameters). Discharge Auger RPM Moisture Content (Xv.b.) 185 30.00 * 25.00 k 20.00-4 15.001 10.00: «1 5.00- — setpoint:18.0 MCavg:15.9 o o' 6 l ---- inlet MC --° Outlet MC llllLlllllA 0.00 T f I f V T j V r V I 1 1'2 23 34 4'5 56 67 76 69 100 Sample Number #— T I r V U I—r i ' I 3 r r r T I 0.00 0.58 1.18 1.74 2.32 2.90 3.48 4.08 4.84 5.22 Time (hr) Figure 6.40: Simulation of the automatic control of a two-stage CCF dryer (Set2) using the W (see Table 4.1 .for dryer parameters) . j 5.80 186 BOJDO 2 1 . g 46.004 1 3 J . a 36.004 . 3 . . § 24.004 - O 1 -l .C 3 12.004 .. ‘3 J 4 0.00 fir r r r T r i I V r f l I T 8 T '— r V 30U00 - I," — setpoint:18.0 MCavg:15.4 4 :5 125430 ..f\ a d 2: .... . . w .1, M , M~~-~-~-~~Mw~1 E 13 004 33'.“ ' ,4 arr—‘— c . "W‘WW . v a 10.00-1 '1 3 * 1 «3 5-00" «4 1m: uc 'j 3 --- Outlet MC 0000 V T r I r I T V r V r r V F V I r 1 12 22 33 43 54 65 75 88 98 107 Sample Number 0.00 0.60 1.50 230 3.10 3.3 4.50 6.60 6.56 7.16 7.06 Time (hr) Figure 6.41: Simulation of the automatic control of a two-stage CCF dryer (Set2) using the Winners! controller (see Table 4.1 for dryer parameters). 187 Table 6.14: Characteristic values of the different control performances with the inlet moisture content variation from Set2 and Set3 and, setpoint equal to 166 w.b.. PERFORMANCE QQIIIQLLlli .....JEL_____ HEASURES 221 MV2 44SsEZ_____E2S1______S2SZ_____S§§1____§§£2___§§£1_ 80(‘Iub.) 1.9 2.0 1.5 1.6 -- -- HDavg(6) 15.9 16.0 15.4 15.6 16.1 16.1 MOmin(6) 10.3 10.4 12.0 12.4 14.7 14.7 M0max(6) 21.0 21.5 20.4 21.4 23.5 22.9 Mlmin(6) 17.6 17.8 17.6 17.8 17.6 17.8 Mlavg(6) 20.7 20.6 20.7 20.6 20.7 20.6 MImax(6) 25.6 25.0 25.6 25.0 25.6 25.0 MIstd(6) 1.1 1.9 1.1 1.9 1.1 1.9 RPHmin 9.0 9.0 11.0 15.0 -- -- RPMavg 35.3 34.6 22.6 22.4 -- -- RPMmax 46.0 46.0 48.0 46.0 -- -- RPHstd 11.9 12.5 6.9 4.6 -- -- 1 for 5 equal to 50. 2 feedback/feedforward with p equal to 0.05 where: PP - pole placement controller minimum variance controller NC - no control (see Figures 6.34 and 6.37) Se - see Eqn.(6.1) N - number of samples (see Table 6.12) N - 106 for Set2 N - 130 for Set3 188 the PP-controller and the MV-controller, respectively. The inlet moisture content fluctuation made it impossible to maintain the outlet moisture content close to the setpoint. However, the controlled cases are better than the uncontrolled case. The simulation run with the PP-controller (see Figure 6.43) resulted in an average outlet moisture content of 166, exactly the desired value. The control error is 26. The frequent change in the discharge auger rpm is because of the rapid change in the inlet moisture content. The controller performance can be considered excellent based on the average outlet moisture content achieved with the large variation in the inlet moisture content. The HV-controller behaved as was expected (see Figure 6.44). The control error Se is 0.26 smaller than that of the PP-controller, and the average moisture content is 15.66, 0.46 from the setpoint. Considering the large variation in the inlet moisture content, the controller performance is good. However, the MV-controller reacts slowly to changes in the inlet and the outlet grain moisture content compared to the PP-controller. In conclusion, the pole placement control system can control a two-stage CCF corn dryer closer to the setpoint than the MV-feedback/ feedforward control. Further advantages with the PP-controller are that it contains few parameters (thus, they can be physically interpreted), and converges rapidly. 6.3) W A series of six tests was conducted with the NV and PP Discharge Auger RPM Moisture Content (Xw.b.) 60.00 * 189 48.00 36.00 24.00 4 12.00 .. 0.00 L ‘ .5 g 5 8 .1 -.. 1...: 1:1,“ n . l ,4.- .-. 2'1, .4,» ..-"-“...:"'.,."1-"- H: , N "J . a‘ ' \ 0w . 0 3' . ‘~~~.‘u h i \’1 .‘MM‘ 1K0“ ‘W’N ’K’V 1, ‘ ’4’ '1‘! r7 “w- ' ---- lnlet MC --- Outlet NC alsLLlalJl V r T T Y— I I T T I 7 r r I fir T f F 1 15 28 42 55 69 82 96 109 123 Sample Number U I— f 1— r r 3 T fiT 3 r 3 T F 0.00 0.88 1.38 2.04 2.72 3.40 4.08 4.78 5.44 8.12 Time (hr) Figure 6.42: Simulation of the automatic control of a two-stage CCF dryer (no control, Set3) (see Table 4.1 for dryer parameters). 190 60.00 2 1 . 0‘: 48.00‘ H 3 . 1 1 g' 36.00 4: § 24.00- 2 1 U U 5 12.004 a . .. 0000 Y I T r U I I I U l' U l U I Y I r r T A 30.00 3° 4 — setpoint: 16.0 MCavg:16.0 4 a 20.00-1 C ‘3 1 . g 15.00- -1 o 1 . 2 10.004 4 3 " 1 .3 53°: --- lnlet uc ‘ 3 --- Outlet 140 ‘ 0.00 V l r r V I I l’ V I I I T I 1— ' I T 1 14 27 41 54 67 80 93 107 120 Sample Number r r I r l T I U r t I 2.16 2.66 3.60 4.52 5.04 5.76 6'46 7720 Time (hr) r 1 I ' 0.00 0.72 1.44 Figure 6.43: Simulation of the automatic control of a two-stage CCF dryer (Set3) using the W (see Table 4.1 for dryer parameters). 191 60.00 2 1 .1 g.- 48.004 .. 6 J 4 0' 36.004 3 1 0 g 24.004 a 1 .1: 1 3. 12.00-J .. o . . 0'00 j V 3 r 3 r 371 3 r f r 3 r 3 r 3 l 3 A 30.00 .a: 25 00-1 — setpoint: 18.0 MCavg:15.8 . 6’. ' 1 .. 1‘6 1...... ..J .1 l 1.16: .. 20.004. ,N' 3" ‘4'? 3 5." 1:63.“. 3.; .33. E 4 J 41.1.“; N%RA11L1‘ I; ‘31 {WA}; 5 15-OO:-——--~---w-«.i' 33“.~w .17...." ‘ em 3: 2 10.004 _ 3 -l .. ’3' 5'00“ - lnlet uc '3 3 0 00 ‘ -- Outlet 110 ‘ '. ' F ' I 3 r 3 r 3 f 3 r 3 r 3 r 3 r T . 1 14 27 40 53 68 79 92 105 1 18 131 Sample Number I 3 r 3 i 3 r m i 3 fi r 3 r f r 3 r 3 1 0.00 0.05 1.00 2.65 3.60 4. 5 5.70 6.65 7.60 6.55 0.50 Time (hr) Figure 6.44: Simulation of the automatic control of a two-stage CCF dryer (Set3) using the MV-feedback/feedforward controller (see Table 4.1 for dryer parameters). 192 controllers on two commercial crossflow dryers over a period of two drying seasons. The controllers controlled the outlet moisture content well even for large inlet moisture content variations. In order to develop an automatic controller for a multi-stage CCF corn dryer, a drying process model was required. Therefore, a differential equation concurrentflow-drying model was developed. The dryer model was used to simulate different control systems. Different empirical models were evaluated in order to determine the best model for on-line control calculations. A simple but accurate linear model was developed for the automatic control of continuous-flow grain dryers. Several control algorithms were analyzed. The pole placement control is stable and accurate; it can be used in any dryer and for any input/output signals. 6.3.1) W Implementation of the proposed control system is simple. It requires the same hardware and software as described in section 5.1.2 with the exception of the moisture meter. In order to use the fixed- distance sample strategy (see section 4.3.1) it is required to have a continuous moisture meter. The software consists of a parameter estimation routine combined with the control algorithm. It requires less than 128k memory capability to run the control system. In addition to the control software, an expression relating rpm and GFR for the particular dryer is needed. If this information can not be found in the dryer specifications of the brochure, these values must be determined at the dryer site. The ..— 193 characteristic of the discharge mechanism must be known in order to give a well defined sample interval. Before the dryer can be switched to automatic mode, the dryer has to run in manual mode for a period of time of about 2 hours in order to obtain acceptable starting values for the control parameters (i.e., recorded input/output values are used to estimate the dryer parameters until they converge to a constant value). However, this procedure is only necessary on the first day of the drying season. On the following days, the input and output variables collected previously are stored on a disk, and can be used to start the control program. Personnel without excessive training can be instructed in the use of the control system in a few days. 6.3.2) We The advantage of the adaptive control system described in this study is that it can be applied to different dryer and cereal types. For a CCF rice dryer, the same models described in section 4.1.1 can be used. In that case, the manipulated variable is the drying air temperature instead of the grain flow rate. For a single-stage dryer, the control strategy is basically the same as used for the CCF corn dryer, i.e, the outlet and inlet moisture content are measured and the control input (inlet air temperature) is adjusted in order to maintain the output as close to the desired value as possible. For a multi-stage dryer, the strategy is more complex because the drying air temperature is different in each stage. One possibility is to set the inlet air temperature to a maximum value in the first stage and control 194 only the last stage using the PP-controller. Another possibility is to control each stage separately using multi-variable systems design. 195 CHAPTER 7 COICLDSIOIS . Control algorithms have been developed for crossflow grain drying using generalized minimum variance and pole placement controllers. . A control system consisting of a microcomputer, a semi-continuous moisture meter, and control software has been implemented and successfully tested on two commercial crossflow grain dryers. . The average outlet moisture content in the commercial dryers was controlled to within 10.30 of the setpoint during two drying seasons. . An unsteady state differential equation simulation model for multi- stage concurrentflow grain drying has been developed. . An adaptive control algorithm has been developed for a two-stage concurrentflow grain dryer. . Different linear models and an exponential model were considered in the design of the control system; the recursive prediction error method was used to estimate the parameters of the linear models. . The model II-b is the best model for predicting the dynamics of continuous-flow grain dryers based on the loss fuction values. 10 ll 12 13 196 . Simulation tests were performed to evaluate the controllers response to different inlet moisture content variations. . The pole placement was selected as the best controller based on simulation results, and is recommended for the automatic control of continuous-flow grain dryers. .The MV-feedback/feedforward controller gives a smaller control error than the PP-controller. However, it reacts slower to changes in working conditions, requires more parameters, and is more complex in than the PP-controller. .The MV-feedback controller shows similar performance as the MV- feedback/feedforward controller. The disadvantage of the former is that it requires more parameters to control the process adequately. .The MV-feedforward controller is considered the least desired system for continuous-flow grain dryers. The MB-controller gives better results than the HV-feedforwerd unit, but it is slow and requires a feedback loop to improve its performances. .The implementation of the proposed system is simple and requires little training. It can be adopted to different dryers and cereal types. 197 CHAPTER 8 SUGGESTIONS FOI.FUTUIB STUDY . To test the recommended controller on a commercial multi-stage concurrentflow corn grain dryer. . To develop different control strategies which would further decrease the variation in the manipulated variable; one possibility is to vary the inlet air temperature in addition to the grain flow rate. . To test the same control system on a concurrentflow rice dryer, i.e., to vary the inlet air temperature instead of the grain flow rate. . 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It is assumed that the process to be controlled is described by: -1 -1 y(z) - niztfl 2" u(z) + A QLZTTl 5 (z) ......... (a.1) A(z ) A(z ) -1 -1 -m where: A(z ) - l + alz + ... + anz -1 -1 -m B(z ) - blz + ... + bnz -1 -1 -m C(z ) - l + clz + ... + cmz m - model order 1 - delay - 0. Here ((k) is a statistically independent signal manuH0143§3338 315(k)} - z - 0 ......... (a.2) 207 It is assumed that w(k) (the reference value) is equal to O, i.e. ew(k) - -y(k). The problem is to design a controller which minimizes the criterion: I(k+1) - E(y’(k+1) + pu’(k)}. ......... (a.3) The controller must generate an input u(k) such that the errors induced by the noise process [£(k)] are minimized according to Eqn.(a.3). In the performance function I, y(k+1) is taken insteady of y(k), as u(k) can only influence the controlled variable at time (k+1) because of the assumption bo-O. Therefore, y(k+l) must be predicted on the basis of known signal values y(k), y(k-l), ... and u(k), u(k-l), ... . Using Eqn (a 1). a aredistien of y(k+1) is: -1 -1 z y(z) - anjTl z u(z) + 1 912771 z {(2) ........ (a.4) A(z ) A(z ) and A(z'1)z y(z) - B(z'l)z u(z) + C(z'1)z {(z) ......... (a.5) or -‘ -m -‘ -m (1+axz +...+anz )z y(z) - (b,z +...+bnz )z u(z) -1 .. + A(l+c12 +...+cnz ll)z €(z). ......... (a.6) After multiplying and transforming back to the time domain, we obtain: y(k+1) + a,y(k) +...+ any(k-m+1) - b,u(k) +...+bn(k-m+l) + A[£(k+1) + c,£(k) +...+ cn(k-m+l)] ......... (a.7) 208 Therefore, the performance criterion of Eqn.(a.3) becomes: I(k+1) - E{[-a1y(k)-...-any(k-m+l) + b1u(k)+...+bnu(k-m+l) + A(c1£(k)+...+cm(k-m+l)) + 1£(k+1)]2 + pu2(k)} ......... (a.8) At time instant k, all signal values are known with the exception of u(k) and ((k+1). Therefore, the expectation of ((k+1) only must be taken. In addition, {(k+1) is independent of all other signal values: I(k+1) - {-a1y(k)-...-any(k-m+1) + b,(k-1)+...+bm(k-m+1) + A[c,$(k)+...+cn§(k-m+1)]2 + A’E{€’(k+1)) + 211-a,y(k)-...+bn(k-m+1) + A[c,£(k)+...+cn(k-m+1)]}E{£(k+l)) + pu2(k). ......... (a.9) Therefore, the condition for optimal u(k) becomes: d§fi%§}l - 21-a,y(k)-...-any(k-m+l) + b1u(k)+b,u(k-l)+...+bn(u-k+l) + A[c1£(k)+...+c'£(k-m+1)])b1 + Zpu(k) - 0 ' ........ (a.10) In this equation, the term in braces before b1 can be replaced using Eqn.(a.7), giving: 209 [zy(2) - AZ€(z)lb: + pu(2) - 0 Applying Eqn.(a.4): 15(2) _ Aiz__l .Biz__l ,1 zy(2) - ,1 zu(2) C(z ) C(z ) then: 3111 1§Iz__1;_Aiz__llz G ( ) - - mv z y(z( zB(z'1)+ fiIC(z'1) ........ (a.12) ........ (a.13) 210 APPENDIX.B: DESCRIPTION OF THE PROCEDURE TO DETERMINE THE RELATIONSHIP BETWEEN RPM AND RESIDENCE TIME FOR CONTINUOUS-FLOW GRAIN DRYERS. Table B.1 presents the experimental data obtained with the Meyer-Morton 850 crossflow dryer. Table B.1: Experimental data for the Meyer-Morton 850 crossflow dryer. 330 1.40 13,900 3.55 430 1.65 17,240 2.86 530 1.90 20,560 2.40 620 2.15 24,460 2.02 720 2.40 28,360 1.74 820 2.64 34,080 1.45 It is assumed that the relationship between the RPM and GRF can be described by a linear equation of this type: 6 GFR (ft /hr) - C1* (RPM) + C, ......... (b.1) The value of the constants C, and C, can be determined by a linear curve fitting method or by plotting GFR vs RPM in a linear paper and find the slope of the curve. For this particular case, C; was found to be equal 0.897 and C2 - 0. To determine the relationship between the residence time (Tr) and the RPM, the following procedure was used: 211 (l) recall that: Tr - l/rpm ........ (b.2) where Tr is in hour. s (2) Cl - 0.897 (ft /rpm-hr) (3) the volume of grain in the dryer is equal to: s Volume - GFR(ft /hr) * residence time (hr) ........ (b.3) (4) then: Volume - 01*RPM.*Tr ........ (b.4) (5) thus, from Eqn.(b.4) it is obtained: Volume/C1 Tr - RPM ........ (b.5) (6) for the Meyer-Morton, the dryer holding capacity is 880 bushel, and s s the volume of grain is then: 880 bu * 1.25 (ft ) - 1100 ft . Therefore, the residence time for a given RPM for the Meyer-Morton dryer can be determined by the following equation: 212 T - 4.221.311. ........ (b.6) (7) The volume of grain to be discharged during a sample interval is equal to the total volume divided by the number of dryer layers. By considering that the dryer is divided in 10 layers, the sample time is then: 421.13.. tr - RPM ........ (b.7) where tr is in hours. The values of the constants in Eqn.(5.6) can be determined by a linear curve-fitting method; here they were found to be equal to: Voltage - 0.565 + 0.002543* (RPM) ........ (b.8) The same procedure is used to determine the residence time as a function of rpm for the Zimmerman dryer and the two-stage CCF drye. HICHIGRN STRTE UNIV. 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