Direct controller designs from plant data

DIRECT CONTROLLER DESIGNS FROM PLANT DATA XU BU B.Sc., BUCT A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF CHEMICAL & BIOMOLECULAR ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2007 ACKNOWLEDGMENT The completion of this thesis is primarily attributed to the keen supervision and constructive direction of my supervisor, Dr. Chiu Min-Sen, to whom I feel most grateful. His academic excellence and meticulous attitude set an exemplar for my future life. Next I would like to pay thankfulness to my labmates, Mr. Yasuki Kansha and Mr. Martin Hermanto. Mr. Kansha provides valuable suggestions on my project, Matlab simulations and the usage of Latex, and Mr. Hermanto helps me with my thesis editing. Also my thanks to Dr. Jia Li (who initiated my originally assigned research), Mr. Ye Myint Hlaing and Ankush Ganeshreddy Kalmukale and Ms. Yang Xin (who helps finalize the submission) and Imma Nuella. The whole bunch of my friends in Singapore contributed to this project with their encouraging friendship, and thus deserves to be listed here with gratitude. Besides those mentioned above, they are: Liu Xiao, Khew Shih Tak, Yin Xiangning, Wang Ke, Wang Likui, Li Jianguo, Tian Xiaoning, Zhou Weihua, Zhang Yi, Dai Taofang, Yao Kexin, Dai Xuexin, Liu Hongyu, Xie Yi, Tan Jing, Zhang Xinhui, Ma Hua, Malik, Sadesh, Ricky Tan, Maxine Lee, Zhang Xingui, Shen Zhigang, etc. Lastly, this research was sponsored by NUS Research Scholarship for nine months and by NUS Graduate Student Tutorship for fifteen months. The generosity of National University of Singapore and its Department of Chemical and Biomolecular Engineering is appreciated. i TABLE OF CONTENTS ACKNOWLEDGEMENTS i TABLE OF CONTENTS ii SUMMARY iv NOMENCLATURE vi LIST OF FIGURES viii LIST OF TABLES xii CHAPTER 1. INTRODUCTION 1 1.1 Motivations 1 1.2 Contributions 6 1.3 Thesis Organization 7 CHAPTER 2. LITERATURE REVIEW 8 2.1 Data-based Controller Design Methods 8 2.2 Model-based PID Design 13 2.3 Internal Model Control 16 CHAPTER 3. DATA-BASED PID CONTROLLER DESIGN 18 3.1 Introduction 18 3.2 Data-based Design of PID Controller 20 3.3 Examples 27 3.4 Conclusion 46 ii CHAPTER 4. DATA-BASED INTERNAL MODEL CONTROL DESIGN 58 4.1 Data-based IMC Design 58 4.2 Examples 65 4.3 Conclusion 74 CHAPTER 5. CONCLUSION 76 REFERENCES 78 iii SUMMARY In this study, data-based approaches derived from VRFT framework are developed for PID and IMC controller designs. In PID design, an open-loop experiment using pulse input signal is first conducted to generate the process input and output data. Subsequently, Discrete Fourier Transform is applied to the process input and output data to obtain their respective frequency responses. The frequency responses data thus obtained are then used to approximate a specified reference model by using an adjustable parameter in the reference model, which is to be determined to provide the best approximation. After determination of the optimal parameter in reference model, the PID controller parameters are subsequently obtained through the least square solution. Though this method requires less design effort than the conventional two-step model-based PID design methods, extensive simulation results show that the resulting PID controller designed off-line by the proposed method gives comparable or better control performance compared to its model-based counterparts, i.e. IMC-PID and Maclaurin-PID controllers, that have been tuned on-line to achieve their respective best control performances. In the proposed data-based IMC design, by using the frequency responses data as mentioned above, a one-step design procedure for IMC controller is developed. Specifically, the parameters of both IMC controller and model are determined simultaneously by solving an optimization problem derived from model-reference problem formulated in the frequency domain. Thus, a distinct feature of the proposed IMC design is that a detailed IMC model is not required to design the IMC controller. Simulation results show that the proposed IMC controller performs as good as or iv better than the conventional IMC controller that has been tuned on-line to produce the best control performance. In summary, the proposed one-step data-based design methods produce high control performance without resorting to the tedious identification of a process model and the need for on-line tuning of controller parameters in an ad-hoc manner. Therefore, from practical application point of view, the proposed data-based PID and IMC designs are attractive alternatives to their respective model-based counterparts. v NOMENCLATURE C PID Controller f Low-pass filter J Objective function L Reference model M Model of the process M Minimum phase of M M Non-minimum phase of M P Process Q IMC controller R, r ~ R, ~ r Set-point T Complementary sensitivity function U, u Process input ~ U , u~ Virtual input W Column vector in Eq. (3.10) X ~ Y, y Column vector in Eq. (4.13) Virtual reference signal Process output Greek Symols , , ~ ~ , IMC controller parameters Matrices used in Eq. (3.10) Adjustable parameter in reference model m Time delay in IMC process model Adjustable parameter in IMC-PID and Maclaurin-PID designs IMC filter constant c ~ IMC Matrix used in Eq. (4.13) Frequency vi B Bandwidth frequency Abbreviations DFT Discrete Fourier Transform FOPDT First-order-plus-dead-time model IAE Integral absolute error IFT Iterative feedback tuning IMC Internal model control PID Proportional-integral-derivative SOPDT Second-order-plus-dead-time model VRFT Virtual reference feedback tuning vii LIST OF FIGURES Figure 1.1 Comparison of M 1 ( s ) and M 2 ( s ) 3 Figure 1.2 Comparison of two controllers derived from M 1 ( s ) and 4 M 2 (s) Figure 2.1 Reference model 11 Figure 2.2 Discrete time feedback system 11 Figure 2.3 IMC structure 17 Figure 3.1 Reference model 22 Figure 3.2 Feedback system 22 Figure 3.3 Input and output signals from the open-loop test (example 27 1) Figure 3.4 Effect of  on J ( ) (example 1) 28 Figure 3.5 Step responses of the process and two models (example 1) 29 Figure 3.6 Set-point responses of the proposed design and model- 30 based designs based on a FOPDT model (example 1) Figure 3.7 Set-point responses of the proposed design and model- 31 based designs based on a SOPDT model (example 1) Figure 3.8 T ( j ) for the reference model and feedback system 32 (example 1) Figure 3.9 Output data of open-loop test under  5% process noise 33 Figure 3.10 Set-point responses of the proposed design under  5% and 33  2% (bottom) process noise (example 1) Figure 3.11 Output signal from the open-loop test (example 2) 34 Figure 3.12 Effect of  on J ( ) (example 2) 35 viii Figure 3.13 Step responses of the process and two models (example 2) 35 Figure 3.14 Set-point responses of the proposed design and model- 36 based designs based on a FOPDT model (example 2) Figure 3.15 Set-point responses of the proposed design and model- 37 based designs based on a SOPDT model (example 2) Figure 3.16 T ( j ) for the reference model and feedback system 38 (example 2) Figure 3.17 Output data of open-loop test under  5% process noise 39 Figure 3.18 Set-point responses of the proposed design under  5% and 39  2% (bottom) process noise (example 2) Figure 3.19 Output signal from the open-loop test (example 3) 40 Figure 3.20 Effect of  on J ( ) (example 3) 41 Figure 3.21 Step responses of the process and two models (example 3) 42 Figure 3.22 Set-point responses of the proposed design and model- 42 based designs based on a FOPDT model (example 3) Figure 3.23 Set-point responses of the proposed design and model- 43 based designs based on a SOPDT model (example 3) Figure 3.24 Set-point responses of the proposed design and model- 44 based design by Huang (example 3) Figure 3.25 T ( j ) for the reference model and feedback system 45 (example 3) Figure 3.26 Output data of open-loop test under  5% process noise 45 Figure 3.27 Set-point responses of the proposed design under  5% and 46  2% (bottom) process noise (example 3) ix Figure 3.28 Set-point responses of the proposed design and model- 47 based designs based on a FOPDT model (example 4) Figure 3.29 Set-point responses of the proposed design and model- 48 based designs based on a SOPDT model (example 4) Figure 3.30 Set-point responses of the proposed design and model- 48 based designs based on a FOPDT model (example 5) Figure 3.31 Set-point responses of the proposed design and model- 49 based designs based on a SOPDT model (example 5) Figure 3.32 Set-point responses of the proposed design and model- 49 based designs based on a FOPDT model (example 6) Figure 3.33 Set-point responses of the proposed design and model- 50 based designs based on a SOPDT model (example 6) Figure 3.34 Set-point responses of the proposed design and model- 50 based designs based on a FOPDT model (example 7) Figure 3.35 Set-point responses of the proposed design and model- 51 based designs based on a SOPDT model (example 7) Figure 3.36 Set-point responses of the proposed design and model- 51 based designs based on a FOPDT model (example 8) Figure 3.37 Set-point responses of the proposed design and model- 52 based designs based on a SOPDT model (example 8) Figure 3.38 Set-point responses of the proposed design and model- 52 based designs based on a FOPDT model (example 9) Figure 3.39 Set-point responses of the proposed design and model- 53 based designs based on a SOPDT model (example 9) Figure 4.1 Reference model 59 x Figure 4.2 IMC structure 61 Figure 4.3 Set-point responses of two IMC designs (example 1) 66 Figure 4.4 T ( j ) for the reference model and IMC system (example 67 1) Figure 4.5 Set-point responses of the proposed design under  5% and 68  2% (bottom) process noise (example 1) Figure 4.6 Set-point responses of two IMC designs (example 2) 70 Figure 4.7 T ( j ) for the reference model and IMC system (example 70 2) Figure 4.8 Set-point responses of the proposed design under  5% and 71  2% (bottom) process noise (example 2) Figure 4.9 Output signal from the open-loop test (example 3) 72 Figure 4.10 Set-point responses of two IMC designs (example 3) 73 Figure 4.11 T ( j ) for the reference model and IMC system (example 73 3) Figure 4.12 Output data of the open-loop test under  5% process noise 74 (example 3) Figure 4.13 Set-point responses of the proposed design under  5% and  2% (bottom) process noise (example 3) xi 75 LIST OF TABLES Table 3.1 PID Controllers obtained by various design methods 53 (example 1) Table 3.2 PID Controllers obtained by various design methods 54 (example 2) Table 3.3 PID Controllers obtained by various design methods 54 (example 3) Table 3.4 Process transfer functions and models in examples 4-9 55 Table 3.5 PID Controllers obtained by various design methods 55 (example 4) Table 3.6 PID Controllers obtained by various design methods 56 (example 5) Table 3.7 PID Controllers obtained by various design methods 56 (example 6) Table 3.8 PID Controllers obtained by various design methods 57 (example 7) Table 3.9 PID Controllers obtained by various design methods 57 (example 8) Table 3.10 PID Controllers obtained by various design methods 57 (example 9) Table 4.1 IMC controllers obtained by two design methods (example 66 1) Table 4.2 IMC controllers obtained by two design methods (example 2) xii 69 Table 4.3 IMC controllers obtained by two design methods (example 3) xiii 72 [...]... Table 3.7 PID Controllers obtained by various design methods 56 (example 6) Table 3.8 PID Controllers obtained by various design methods 57 (example 7) Table 3.9 PID Controllers obtained by various design methods 57 (example 8) Table 3.10 PID Controllers obtained by various design methods 57 (example 9) Table 4.1 IMC controllers obtained by two design methods (example 66 1) Table 4.2 IMC controllers... TABLES Table 3.1 PID Controllers obtained by various design methods 53 (example 1) Table 3.2 PID Controllers obtained by various design methods 54 (example 2) Table 3.3 PID Controllers obtained by various design methods 54 (example 3) Table 3.4 Process transfer functions and models in examples 4-9 55 Table 3.5 PID Controllers obtained by various design methods 55 (example 4) Table 3.6 PID Controllers obtained... design and model- 51 based designs based on a FOPDT model (example 8) Figure 3.37 Set-point responses of the proposed design and model- 52 based designs based on a SOPDT model (example 8) Figure 3.38 Set-point responses of the proposed design and model- 52 based designs based on a FOPDT model (example 9) Figure 3.39 Set-point responses of the proposed design and model- 53 based designs based on a SOPDT... design and model- 47 based designs based on a FOPDT model (example 4) Figure 3.29 Set-point responses of the proposed design and model- 48 based designs based on a SOPDT model (example 4) Figure 3.30 Set-point responses of the proposed design and model- 48 based designs based on a FOPDT model (example 5) Figure 3.31 Set-point responses of the proposed design and model- 49 based designs based on a SOPDT... design and model- 49 based designs based on a FOPDT model (example 6) Figure 3.33 Set-point responses of the proposed design and model- 50 based designs based on a SOPDT model (example 6) Figure 3.34 Set-point responses of the proposed design and model- 50 based designs based on a FOPDT model (example 7) Figure 3.35 Set-point responses of the proposed design and model- 51 based designs based on a SOPDT... the proposed design under  5% and 71  2% (bottom) process noise (example 2) Figure 4.9 Output signal from the open-loop test (example 3) 72 Figure 4.10 Set-point responses of two IMC designs (example 3) 73 Figure 4.11 T ( j ) for the reference model and IMC system (example 73 3) Figure 4.12 Output data of the open-loop test under  5% process noise 74 (example 3) Figure 4.13 Set-point responses of... 59 x Figure 4.2 IMC structure 61 Figure 4.3 Set-point responses of two IMC designs (example 1) 66 Figure 4.4 T ( j ) for the reference model and IMC system (example 67 1) Figure 4.5 Set-point responses of the proposed design under  5% and 68  2% (bottom) process noise (example 1) Figure 4.6 Set-point responses of two IMC designs (example 2) 70 Figure 4.7 T ( j ) for the reference model and IMC... various design methods 57 (example 9) Table 4.1 IMC controllers obtained by two design methods (example 66 1) Table 4.2 IMC controllers obtained by two design methods (example 2) xii 69 Table 4.3 IMC controllers obtained by two design methods (example 3) xiii 72  ... Data- based Controller Design Methods 2.2 Model-based PID Design 13 2.3 Internal Model Control 16 CHAPTER DATA- BASED PID CONTROLLER DESIGN 18 3.1 Introduction 18 3.2 Data- based Design of PID Controller. .. proposed data- based IMC design, by using the frequency responses data as mentioned above, a one-step design procedure for IMC controller is developed Specifically, the parameters of both IMC controller. .. the need for on-line tuning of controller parameters in an ad-hoc manner Therefore, from practical application point of view, the proposed data- based PID and IMC designs are attractive alternatives