DIGITAL DATA-BASED PID CONTROLLER DESIGN FOR PROCESSES WITH INVERSE RESPONSE XU YUNCHEN NATIONAL UNIVERSITY OF SINGAPORE 2015 DIGITAL DATA-BASED PID CONTROLLER DESIGN FOR PROCESSES WITH INVERSE RESPONSE XU YUNCHEN (B Eng (Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2015 DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety I have duly acknowledged all the sources of information which have been used in the thesis This thesis has also not been submitted for any degree in any university previously XU YUNCHEN 09 Jan 2015 ACKNOWLEDGEMENTS First and foremost, I would like to thank my supervisor, Prof Chiu Min-Sen for his guidance, encouragement, patience, support and invaluable time in helping me for my research and studies in the National University of Singapore His kindness and special help regarding not only my study but also my life are really appreciated Furthermore, I would like to express my deepest gratitude to Prof Chiu Min-Sen for his painstaking revision of this thesis Special thanks and appreciation are due to my lab mates, Su Qinglin, Vamsi Krishna Kamaraju, Huang Wen and Liu Haoliang for helpful discussions that we have had and the helps they have offered to me Additionally, I would like to thank Wang Zhi Hao for the stimulating discussions that contributes to my research work I also extend my sincere thanks to the administrative staff in the Department of Chemical and Biomolecular Engineering who have helped me Last but not the least, I offer my thanks to my parents and my friends for their understanding and encouragement, without which my may not be able to complete my research work i TABLE OF CONTENTS ACKNOWLEDGEMENTS i TABLE OF CONTENTS ii SUMMARY iv LIST OF TABLES v LIST OF FIGURES vi NOMENCLATURE ix CHAPTER INTRODUCTION 1.1 Motivations 1.2 Contributions Applied 1.3 Thesis Organization CHAPTER LITERATURE REVIEW 2.1 Direct Data-based Controller Design Methods 2.2 Adaptive Control 10 2.3 Control of Inverse Response 13 CHAPTER VRFT DESIGN OF PID CONTROLLERS FOR STABLE PROCESSES WITH INVERSE RESPONSE 15 3.1 Introduction 15 3.2 The Proposed VRFT Design Method 16 3.3 Simulation Results 19 ii 3.4 Conclusion 38 CHAPTER EVRFT DESIGN OF ADAPTIVE PID CONTROLLERS FOR STABLE PROCESSES WITH INVERSE RESPONSE 39 4.1 Introduction 39 4.2 VRFT Design of PID Controllers Using New Reference Models 40 4.3 Enhanced VRFT Design Method 43 4.4 Simulation Results 45 4.5 Conclusion 55 CHAPTER CONCLUSIONS AND FURTHER WORK 56 5.1 Conclusions 56 5.2 Suggestions for Further Work 57 REFERENCE 58 Appendix 63 iii SUMMARY Controller design for processes with inverse response has attracted interest from control community since high control performance of feedback control systems is more difficult to achieve for such processes Inverse response, which is resulted from the dynamic effect of a right-half-plane (RHP) zero, leads to smaller margin to guard against closed-loop instability and consequently the loss of control performance as a result Various model-based controller design methods have been developed in the literature, however, the control performance may become unsatisfactory when processes are higher-order with small value of RHP zero In this thesis, a one-step method for discrete-time proportional-integral-derivative (PID) controller design is developed within the virtual reference feedback tuning (VRFT) framework to handle processes with inverse response In the proposed method, a newly developed second-order plus time delay reference model with one RHP zero is employed for VRFT design of PID controller for processes with inverse response Simulation results show that the control performance is improved by using the proposed design method compared to the benchmark designs consisting of both model-based design method and the existing VRFT design methods which not take RHP zero into account in formulating the control algorithm Furthermore, the proposed method is extended to the nonlinear processes with inverse response It is evident from simulation results that the proposed design provides improved performance iv LIST OF TABLES Table 3.1 Comparison of the three controllers designed for G1-8 21 Table 3.2 Comparison of the three controllers designed for G1-2, 22 G1-4 and G1-16 Table 3.3 Comparison of the three controllers designed for G2-γ 24 Table 3.4 Comparison of the three controllers designed for G3-γ 26 Table 3.5 Comparison of the three controllers designed for G4-γ 28 Table 3.6 Comparison of the three controllers designed for G5-γ 30 Table 3.7 Comparison of the three controllers designed for G6-γ 32 Table 3.8 Comparison of the three controllers designed for G7-γ 34 Table 3.9 Comparison of the three controllers designed for G8-γ 36 Table 4.1 Summary of tuning parameters for the proposed 47 EVRFT design Table 4.2 Tracking errors for various design methods 48 Table 4.3 Tracking errors for various design methods for time 54 delay case v LIST OF FIGURES Figure 2.1 Reference model Figure 2.2 Feedback control system Figure 2.3 Diagram of adaptive control scheme 11 Figure 3.1 Input and output signals generated for the 20 process G1-8 Figure 3.2 Servo response of the three controllers designed 21 for G1-8 Figure 3.3 Servo response of the three controllers designed 23 for G1-2, G1-4 and G1-16 Figure 3.4 Servo response of the three controllers designed 25 for G2-γ Figure 3.5 Servo response of the three controllers designed 27 for G3-γ Figure 3.6 Servo response of the three controllers designed 29 for G4-γ Figure 3.7 Servo response of the three controllers designed 31 for G5-γ Figure 3.8 Servo response of the three controllers designed 33 for G6-γ Figure 3.9 Servo response of the three controllers designed vi 35 for G7-γ Figure 3.10 Servo response of the three controllers designed 37 for G8-γ Figure 4.1 Steady-state curve of van de Vusse reactor 46 Figure 4.2 Input-output data used for constructing the 46 database for EVRFT design Figure 4.3 Servo performance for set-point changes from 49 1.12 to 1.25 Figure 4.4 Servo performance for set-point changes from 49 1.12 to 0.62 Figure 4.5 Updating of controller parameters in proposed 50 (first-order) for set-point change to 1.25 Figure 4.6 Updating of controller parameters in proposed 50 (second-order) for set-point change to 1.25 Figure 4.7 Updating of controller parameters in proposed 51 (first-order) for set-point change to 0.62 Figure 4.8 Updating of controller parameters in proposed 51 (second-order) for set-point change to 0.62 Figure 4.9 Responses for set-point from 1.12 to 1.25 in the 52 presence of modeling error Figure 4.10 Responses for set-point from 1.12 to 0.62 in the presence of modeling error vii 52 Chapter EVRFT Design of Adaptive PID Controllers for Stable Processes with Inverse Response Figure 4.3 Servo performance for set-point change from 1.12 to 1.25 Figure 4.4 Servo performance for set-point change from 1.12 to 0.62 49 Chapter EVRFT Design of Adaptive PID Controllers for Stable Processes with Inverse Response Figure 4.5 Updating of controller parameters in proposed (first-order) for set-point change to 1.25 Figure 4.6 Updating of controller parameters in proposed (second-order) for set-point change to 1.25 50 Chapter EVRFT Design of Adaptive PID Controllers for Stable Processes with Inverse Response Figure 4.7 Updating of controller parameters in proposed (first-order) for setpoint change to 0.62 Figure 4.8 Updating of controller parameters in proposed (second-order) for set-point change to 0.62 51 Chapter EVRFT Design of Adaptive PID Controllers for Stable Processes with Inverse Response Furthermore, 20% modeling error in the kinetic parameter 𝑘1 and 𝑘2 is assumed to test the robustness of the proposed control strategy Figure 4.9 and 4.10 show that the two proposed EVRFT design methods give satisfied performance in the presence of such modeling error Figure 4.9 Responses for set-point from 1.12 to 1.25 in the presence of modeling error Figure 4.10 Responses for set-point from 1.12 to 0.62 in the presence of modeling error 52 Chapter EVRFT Design of Adaptive PID Controllers for Stable Processes with Inverse Response Finally, it is assumed that there exists time delay in the output measurement of five sampling time The controllers’ performance from various design methods are evaluated according the parameter specifications presented in Table 4.1 Figure 4.11 and 4.12 illustrate the resulting performances of EVRFT design for the same set-point changes described previously EVRFT design (Yang et al., 2012) and VRFT design method proposed in Chapter are used for comparison purpose The summary of tracking errors for different design methods are presented in Table 4.3 It is clear that the proposed EVRFT design methods give better or comparable control performance than other benchmark design methods Table 4.3 Tracking errors for various design methods for time delay case Set point change to 1.25 Tracking Error Improvement Proposed (second-order) 2.00*10-3 Proposed Proposed Proposed (first-order) 1.91*10-3 (second-order) (first-order) EVRFT 2.10*10-3 4.76% 6.19% VRFT 3.10*10-3 35.48% 38.39% Set point change to 0.62 Tracking Error Improvement Proposed (second-order) 1.12*10-2 Proposed Proposed Proposed (first-order) 7.65*10-3 (second-order) (first-order) EVRFT 1.72*10-2 34.88% 55.52% VRFT Unstable - - 53 Chapter EVRFT Design of Adaptive PID Controllers for Stable Processes with Inverse Response Figure 4.11 Response for set-point from 1.12 to 1.25 for time delay case Figure 4.12 Response for set-point from 1.12 to 0.62 for time delay case 54 Chapter EVRFT Design of Adaptive PID Controllers for Stable Processes with Inverse Response 4.5 Conclusion In this chapter, two adaptive PID controller deign methods are proposed The proposed methods use VRFT design framework at each sampling instance and achieves the adaptive nature by updating the database, choosing a relevant dataset as well as updating the reference model parameter at each sampling instance Furthermore, the first and second-order reference model plus time delay with one RHP zero are applied for the VRFT design for better performance of process with inverse response The simulation results show that both proposed methods give better or comparable control performance than the conventional EVRFT design and VRFT design methods 55 Chapter Conclusions and Further Work Chapter Conclusions and Further Work 5.1 Conclusions In this thesis, new discrete time first and second-order plus time delay reference model by incorporating one right-half-plane (RHP) zero are proposed and derived for VRFT and EVRFT design frameworks to deal with process with inverse response Firstly, a second-order plus time delay reference model with one RHP zero is derived and employed for the VRFT design of discrete time PID controllers for processes with inverse response dynamics Secondly, two new reference models incorporating one RHP zero are employed under the EVRFT design framework for controlling the nonlinear processes exhibiting inverse response dynamics The EVRFT design framework updates not only the database but also the parameters in the reference model at each sampling instance during the control process to achieve better performance Simulations results presented show that both PID controller and adaptive PID controllers proposed give faster and less oscillatory responses than various benchmark design methods In summary, the proposed VRFT and EVRFT design methods are useful strategies for linear and nonlinear processes with inverse response dynamics 56 Chapter Conclusions and Further Work 5.2 Suggestions for Further Work There still remain several research topics that need to be further studied, which are summarized in the following (1) The proposed PID controller design method in Chapter uses a second-order reference model plus time delay with one RHP zero containing two tuning variables γ and A The Eq (3.14) solve the quadratic optimization problem to find the PID controller by tuning A and γ However, it may cost less computational time if the value of optimal γ can be obtained in open-loop process by measuring the real value of the RHP zero of the controlled process By reducing one tuning variable, the VRFT design framework may process faster Some simulation results of applying the proposed method to Hammerstein system have been obtained with good performance More simulation should be conducted in order to widen the application of proposed PID controller design method (2) The proposed adaptive PID controllers designed in Chapter are only applied to chemical process van der Vusses reactor due to limited experiment data It may be possible that such adaptive PID controllers can be applied to area such as flight control and power control which exhibit inverse response dynamics 57 Reference REFERENCE 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VRFT Design of PID Controllers for Stable Processes with Inverse Response Figure 3.4 Servo response of the three controllers designed for G2-γ 25 Chapter VRFT Design of PID Controllers for Stable... VRFT Design of PID Controllers for Stable Processes with Inverse Response Figure 3.5 Servo response of the three controllers designed for G3-γ 27 Chapter VRFT Design of PID Controllers for Stable