linear and adaptive controller designs from plant data

LINEAR AND ADAPTIVE CONTROLLER DESIGNS FROM PLANT DATA YANG XIN NATIONAL UNIVERSITY OF SINGAPORE 2011 LINEAR AND ADAPTIVE CONTROLLER DESIGNS FROM PLANT DATA YANG XIN (B. Eng., M. Eng., Qingdao University of Science and Technology, China) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2011 ACKNOWLEGEMENTS Firstly, I owe my deepest gratitude to my supervisor, Prof. Chiu Min-Sen, whose guidance, encouragement, patience and support enabled me complete this research work. His rigorous attitude and perseverance in research benefits me. His kindness and consideration regarding my study and my life are much indeed appreciated. My special thanks to Prof. Chiu for his invaluable time to read and revise this thesis. I also would like to heartily thankful to my examiner for my Oral Q.E, Prof. Wang Qing-Guo and Prof. Rudiyanto Gunawan, for their valuable advices to my research work. In addition, I am very indebted to Dr. Koichi Fujiwara and Prof. Manabu Kano at Kyoto University to kindly send me their Co-JITL program to facilitate my research work and their patience to clarify my numerous enquiries about the Co-JITL method. Moreover, I would like to show my gratitude to the Prof. William Bernard Krantz, Prof. Raj Srinivasan, Prof. Karimi, Prof. Lakshminarayanan Samavedham, Prof. Hong Liang, Prof. Tan Thiam Chye for teaching me the course modules. Additionally, I would like to thank the technical and administrative staffs in the Chemical and Biomolecular Engineering Department for the kind assistance. I am also indebted to the National University of Singapore to support me the research scholarships. My sincere thanks to my lab mates: Cheng Cheng, Yasuki Kansha, Martin Wijaya Hermanto, Xu Bu, Imma Nuella, Li Yan, Su Qing Lin, Vamsi Krishna Kamaraju, and Huang Wen. This is a group filled with enjoyable friendships and collaboration, and I will never forget their sincerity and warm-hearted helps. I am also grateful to all my lovely friends and roommates in Singapore whose helps and encouragement will be remembered in my heart. i Chapter Introduction Last but not the least, I offer my thanks to my parents, my sister and brother, and my husband Zhang Xiaodong for their love and encouragement, which give me the strength and determination to pursue my dream and finish my thesis. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS i TABLE OF CONTENTS iii SUMMARY vii LIST OF TABLES viii LIST OF FIGURES xi NOMENCLATURE xvi CHAPTER 1. INTRODUCTION 1.1 Motivations 1.2 Contributions 1.2.1 Controller design methods using the VRFT method 1.2.2 Controller design methods using the JITL technique 1.3 Thesis organization CHAPTER 2. LITERATURE REVIEW 2.1 Data-based nonlinear process modeling 2.1.1 Standard-learning methods 2.1.2 Just-in-Time Learning (JITL) 2.2 Controller Design methods 10 15 2.2.1 Model-based controller design methods 15 2.2.2 Direct data-based controller design methods 20 2.2.3 Adaptive control 24 iii CHAPTER 3. DIRECT DATA-BASED PID CONTROLLER DESIGN 30 3.1 Introduction 30 3.2 Direct data-based PID controller design 32 3.2.1 Specification of T (s ) and ω max 3.3 Examples and results 36 38 3.3.1 Linear processes 38 3.3.2 Nonlinear process 51 3.4 Conclusion 55 CHAPTER 4. ALTERNATIVE DIRECT PID DESIGN USING L(S) 57 4.1 Introduction 57 4.2 Proposed PID design using L(s) 57 4.2.1 Specification of L(s ) and ω max 4.3 Examples and results 60 62 4.3.1 Linear processes 62 4.3.2 Nonlinear process 65 4.4 Conclusion CHAPTER 5. ONE-STEP IMC DESIGN DIRECTLY FROM PLANT 68 69 DATA 5.1 Introduction 69 5.2 VRFT-based IMC controller design 70 5.3 Proposed one-step IMC design 82 5.4 Conclusion 89 iv CHAPTER 6. ADAPTIVE PID CONTROLLER DESIGN USING THE 90 EVRFT METHOD 6.1 Introduction 90 6.2 Adaptive PID Controller design by the EVRFT method 91 6.2.1 PID controller design by the VRFT method 91 6.2.2 Enhanced VRFT method (EVRFT) 94 6.3 Examples and results 6.4 Conclusion CHAPTER 7. SELF-TUNING DECENTRALIZED PID CONTROLLER 96 108 109 DESIGN FOR MULTIVARIABLE SYSTEMS 7.1 Introduction 109 7.2 Self-tuning decentralized PID controller design 111 7.3 Examples and results 116 7.4 Conclusion 136 CHAPTER 8. ADAPTIVE PID DESIGN DIRECTLY USING JITL 137 METHOD 8.1 Introduction 137 8.2 JITL-based adaptive PID controller design 138 8.3 Examples and results 141 8.4 Comparison of two proposed adaptive PID controllers 148 8.5 Conclusion 150 v CHAPTER 9. CONCLUSIONS AND FUTURE WORK 151 9.1 Conclusions 151 9.2 Future work 153 REFERENCES 155 PUBLICATION AND PRESENTATION 166 vi SUMMARY In this thesis, several data-based linear and adaptive control strategies have been developed using the Virtual Reference Feedback Tuning (VRFT) method and the Just-in-Time Learning (JITL) technique, respectively. The main contributions of this thesis are as follows. Firstly, by extending the VRFT design framework to the continuous time systems, its application to PID controller design leads to a direct PID design method using the process data available from open-loop tests. The PID parameters are obtained by solving an optimization problem formulated in the frequency domain without resorting to the availability of a process model. However, the application of the VRFT design framework to IMC design does not produce better control performance compared with the conventional IMC design. To improve the VRFT-based IMC design, the proposed one-step IMC design develops three correlation equations to obtain the parameters of IMC model and controller based on one key parameter obtained by the VRFT-based IMC design. In the proposed one-step IMC design method, the IMC model and controller are designed simultaneously, which is in a sharp contrast with the conventional IMC design that requires the availability of IMC model preceding the design of IMC controllers and the trial-and-error procedure for tuning of the IMC filter at the expense of considerable engineering efforts. Furthermore, an enhanced VRFT (EVRFT) method is proposed with its application to an adaptive PID controller design. In the EVRFT design, a secondorder reference model is employed instead of the first-order reference model commonly used in the literature. In addition, other than the update of reference vii database, the parameter in the reference model is also updated at each sampling instance to further improve the resulting control performance. By incorporating the JITL technique into controller design, a self-tuning decentralized PID controller design method for multivariable system is developed. In this method, a set of linear models obtained by the JITL provides the information required to adjust the parameters of decentralized PID controller by an updating algorithm derived by the Lyapunov method such that the JITL's predicted tracking error converges asymptotically. Finally, a new adaptive PID controller design method is developed by utilizing the JITL technique directly, without resorting to the common use of JITL as an estimator for process dynamics. In the proposed design, the reference database is built by using the open-loop data and a closed-loop reference model, and the PID algorithm is treated as the local model by the JITL method. In this respect, the JITL method is employed to learn the mapping between the relevant inputs and desired outputs of the PID controller. Consequently, the PID parameters are updated online by virtue of adaptive nature of JITL technique by choosing the relevant dataset from the reference database according to the query data based on the current and past feedback errors. Simulation results are presented to demonstrate that the proposed control strategies give comparable or better performance than their respective conventional counterparts. viii Chapter Conclusions and Future Work Chapter Conclusions and Future Work 9.1 Conclusions In this thesis, several linear and adaptive controller design methods are developed by using VRFT and JITL techniques. Firstly, a direct data-based PID controller design is developed by solving an optimization problem resulting from approximating a reference model T(s) in a systematic one-step procedure. This is a sharp contrast with the IMC-based PID design methods that require the process model identification and trial-and-error procedure to determine the optimal tunable parameter from simulation studies requiring prior information of process dynamics or plant tests, which demand considerable engineering efforts. Extensive simulation results show that the direct data-based PID controller not only outperforms the direct model-based PID designs such as Connell-PID and Skogestad-PID designs, but also gives comparable or better control performance than the IMC-based PID controllers including IMC-PID and Maclaurin-PID designs that have been tuned on-line by trial and error to achieve their respective best control performance. Furthermore, using another reference model based on the desired loop transfer function L(s), an alternative direct data-based PID controller design method is developed. Extensive simulation results show that this alternative PID design using 151 Chapter Conclusions and Future Work L(s) provides comparable control performance with that using the reference model T(s). Motivated by the encouraging results mentioned above, the VRFT design framework is also extended to design IMC controller in continuous time. However, the resulting control performance cannot match to that of conventional IMC controller. To achieve better control performance, the proposed one-step IMC design is developed based on three correlation equations obtained from extensive simulation studies and one key parameter of the VRFT-based IMC design. Contrast to the conventional two-step IMC design that require the process model to be identified prior to the design of IMC controller, this proposed method designs IMC controller and model simultaneously without an iterative two-step design procedure inherent in the conventional IMC design. Simulation results show that the proposed IMC design not only improves the performance of VRFT-based IMC design, but also gives better or comparable performance than that of the conventional IMC design. Next, an adaptive PID controller is developed using the proposed Enhanced Virtual Reference Feedback Tuning (EVRFT) method for nonlinear system. This method makes use of a second-order reference model instead of the first-order reference model normally used in the literature. The controller parameters are designed by updating the database and the parameter in the reference model. Simulation results demonstrate that the proposed adaptive PID design using the EVRFT method gives better response than the conventional VRFT design. Consequently, the EVRFT method is a useful strategy for adaptive controller design for nonlinear processes. A self-tuning decentralized PID controller design utilizing JITL modeling technique is developed for multivariable systems. In this method, PID parameters are 152 Chapter Conclusions and Future Work updated based on the information provided by the JITL and an updating algorithm derived from the Lyapunov method. Simulation results illustrate that the proposed methods have better control performance than their conventional counterparts reported in the literature. Another adaptive PID design method is proposed by using the JITL technique for controller tuning directly, which is the main departure from the common use of JITL as an estimator for process dynamics in the previous work. In this proposed method, reference database that mimics the PID control algorithm is constructed by using the open-loop data and a closed-loop reference model. So the local model determined by the JITL corresponds to the updated PID control algorithm obtained at each sampling instant. Simulation results show that the proposed method has better performance than the PID controller designed by conventional VRFT design, but it is comparable with the other adaptive PID controller design using the EVRFT developed in this thesis. 9.2 Future Work There remain several interesting research topics that warrant further research investigation, which are summarized in the following. (1) The proposed data-based direct PID and one-step IMC controller design methods developed in the VRFT framework only focus on the servo performance in the controller design. Therefore, when the regulatory response is the primary design requirement, it is of significant practical importance to develop new design methods and more importantly new reference models that can reflect better the load performance, which is a challenging topic on its own. In addition, the one-step IMC design method is developed primarily for minimum-phase processes and hence how 153 Chapter Conclusions and Future Work to extend the existing design method for non-minimum phase systems is worthwhile for further investigation. Furthermore, the extension of the proposed data-based designs to the TwoDegree-of-Freedom control system warrants further investigation as well. In addition, the proposed PID and IMC design methods may be extended and generalized to more complicated control systems such as cascade control system or multivariable systems. (2) The adaptive PID controller design directly using JITL technique developed in Chapter is based on the first-order reference model. 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ICCAS-SICE, ICROS-SICE International Joint Conference, Fukuoka, Japan, IEEE Computer Society. Yang, X., Xu B., and Chiu, M. S. (2010). A Data-Based Approach to PID Controller Design. The 5th International Symposium on Design, Operation and Control of Chemical Processes, PSE Asia 2010, Singapore. Yang, X., Xu, B., and Chiu, M. S. (2011). PID controller design directly from plant Data. Industrial & Engineering Chemistry Research, 50, 1352-1359. Yang, X., Jia, L., and Chiu, M. S. (2011). Self-tuning decentralized PID controllers design based on the Lyapunov approach. Journal of Process Control, submitted. Yang, X., Li, Y., Kansha, Y. and Chiu, M. S. (2011). An enhanced VRFT method and its application to adaptive PID controller design. Chemical Engineering Science, submitted. Yang, X., Xu, B., and Chiu, M. S. (2011). One-step IMC design directly from plant data. Industrial & Engineering Chemistry Research, submitted. Yang, X. and Chiu, M. S. Adaptive PID controller design directly using the JITL technique, under preparation. 166 [...]... which may hinder the performance of resulting adaptive controller Therefore, attempts will be made to develop an enhanced version of the VRFT (EVRFT) method to achieve better performance for nonlinear systems in this thesis 1.2 Contributions In this thesis, linear and adaptive controller design methods are developed from plant data using the VRFT method and JITL approach, respectively The main contributions... contributions of this thesis are as follows 1.2.1 Controller design methods using the VRFT method (1) Direct data- based PID controller design A direct data- based PID controller design is developed from the process input and output data collected in an open-loop test, without resorting to the availability of a process model preceding the controller design and trial -and- error procedure necessitated in the IMC-based... obtained by the proposed PID and VRFT designs 144 Table 8.2 Tracking errors obtained by the proposed PID and VRFT designs in the presence of time delay 148 Table 8.3 Tracking errors of the JITL-based and EVRFT-based adaptive PID designs 148 x LIST OF FIGURES Figure 2.1 Comparison of JITL and standard-learning 11 Figure 2.2 Similarity measure between the conventional JITL (left) and Co-JITL (right) 12 Figure... Input-output data used for constructing the database 98 Figure 6.2 Servo response of the EVRFT and VRFT designs 99 Figure 6.3 Updating of tuning parameters in the EVRFT design 100 Figure 6.4 Input-output data used for constructing the database 101 Figure 6.5 Servo response of the EVRFT and VRFT designs 102 Figure 6.6 Updating of tuning parameters in the EVRFT designs for set-point changes from 25000.5... the data used for local modeling are selected on the basis of correlation instead of distance and angle metrics, and they are continuous dynamically in a relevant dataset The difference of the similarity measure in selecting the data between the conventional JITL and Co-JITL is shown in Figure 2.2 In Chapters 7 and 8 of this thesis, Co-JITL will be incorporated in the proposed data- based controller designs. .. technique by choosing the relevant dataset from the reference database according to the query data based on the current and past feedback errors 1.3 Thesis organization This thesis is organized as follows Chapter 2 comprises the literature review of data- based process modeling and control methods By extending the VRFT to continuous time domain, the direct data- based PID controllers are designed using two... model and the current query data The local model is then discarded right after the answer is obtained When the next query data comes, a new local model will be built repeatedly according to the aforementioned procedure Figure 2.1 illustrates the differences between the standard learning and the JITL method Standard Learning Just-in-Time Learning Learning phase Query Data Modeling Tools Query Data Database... proposed PID and VRFT designs in the presence of time delay 147 Figure 8.10 Updating of PID parameters in the proposed design for setpoint changes to 40000 (left) and 12500 (right) in the presence of time delay 147 Figure 8.11 Servo response of the JITL-based and EVRFT-based adaptive PID designs for the CSTR example 149 Figure 8.12 Servo response of the JITL-based and EVRFT-based adaptive PID designs for... Subsequently, this database can be updated during its on-line application, and the new process data will be added to the database to improve its prediction accuracy for new operating region where the process data may not be available to construct the initial database for Co-JITL Suppose that the present Co-JITL’s reference database Z consists of n process data z i = [x i y (i )]i =1~ n Given a query data z q... obtain the local ARX model of the nonlinear systems by focusing on the relevant region around the current operating condition The first step is to select the relevant dataset from the database that resembles the query data To do so, the database is divided into smaller datasets The size of these smaller datasets is specified by the window length, W, such that the i-th dataset is denoted as Z i = [z i  . LINEAR AND ADAPTIVE CONTROLLER DESIGNS FROM PLANT DATA YANG XIN NATIONAL UNIVERSITY OF SINGAPORE 2011 LINEAR AND ADAPTIVE CONTROLLER DESIGNS FROM PLANT. Direct data- based controller design methods 20 2.2.3 Adaptive control 24 iv CHAPTER 3. DIRECT DATA- BASED PID CONTROLLER DESIGN 30 3.1 Introduction 30 3.2 Direct data- based PID controller. )(sL and max ω 60 4.3 Examples and results 62 4.3.1 Linear processes 62 4.3.2 Nonlinear process 65 4.4 Conclusion 68 CHAPTER 5. ONE-STEP IMC DESIGN DIRECTLY FROM PLANT DATA 69