Relay Tuning of PID Controllers (eBook)

M. Chidambaram is currently a Professor at the Department of Chemical Engineering, Indian Institute of Technology in Madras, Chennai. After completing his PhD at the Indian Institute of Science in Bangalore he served as a faculty member at the Indian Institute of Technology Bombay, Mumbai, from 1984 to 1991. Since then he has been a faculty member at the Indian Institute of Technology in Madras. He has also served the institute as Head of the Department of Chemical Engineering from 2000 to 2003 and as the Director, National Institute of Technology (NIT), Tiruchirappalli from 2005 to 2010. He has 190 journal articles, 7 books and 4 book chapters to his credit. His primary research interest is in the area of process control. 'Nikita Saxena completed her PhD' under the guidance of Prof. M Chidambaram. She completed her degree (BTech) in Chemical Technology at Harcourt Butler Technical Institute (HBTI), Kanpur. She also has a year of experience in the fast-moving consumer goods (FMCG) industry. She has authored 4 journal articles and presented papers at several conferences. Her areas of interest include relay control systems and model identification.

Series Editors’ Foreword 7
Preface 9
Acknowledgement 11
Contents 12
About the Authors 16
Abbreviations and Notations 17
List of Figures 19
List of Tables 24
1 Introduction 28
1.1 Scope of Process Control 28
1.2 Proportional–Derivative–Integral Control 29
1.3 Loop Tuning 30
1.3.1 Manual Loop Tuning 31
1.3.2 Ziegler–Nichols Method (1942) 31
1.3.3 Refined Ziegler–Nichols Methods 32
1.3.4 Process Reaction Curve Method 33
1.3.5 Cohen–Coon Method (1953) 34
1.3.6 Synthesis Method 35
1.4 Relay Feedback Method 35
1.5 Real-Time Example 37
1.6 Conclusion 38
References 38
2 Relay Control System 40
2.1 Relay Control System 40
2.2 Describing Function Analysis 42
2.3 Shape of the Relay Waveform 44
2.4 Relay Auto-tuning for Scalar System 45
2.4.1 Modified Relay Feedback Method—Sung et al. (1995) 47
2.4.2 Modified Fourier Series Analysis of Process Response—Srinivasan and Chidambaram (2004) 48
2.4.3 Use of Preload Relay—Tan et al. (2006) 49
2.4.4 Enhanced Process Activation Method—Je et al. (2009) 50
2.4.5 Simulation Study 51
2.5 Tuning of Multivariable System 52
2.5.1 Pairing Criteria 55
2.5.2 Controller Design Using Independent Tuning Method 56
2.6 Relay Feedback Test for Multivariable System 61
2.6.1 Condition for Limit Cycle to Occur 62
2.6.2 Relay Auto-tuning of Decentralized Controllers 63
2.6.2.1 Palmor et al. (1995) 63
2.6.2.2 Zhuang and Atherton (1994) 65
2.6.2.3 Campestrini et al. (2009) 66
2.6.3 Relay Auto-tuning of Centralized Controllers 67
2.6.3.1 Menani and Koivo (1996c) 67
2.6.3.2 Wang et al. (1997) 68
2.6.3.3 Menani (1999) 70
2.7 Design of PID Controllers 70
2.8 Robust Stability Analysis 72
2.9 Conclusion 77
References 77
3 Auto-Tuning of Unstable SOPTD Systems 79
3.1 Introduction 79
3.2 Consideration of Higher Order Harmonics 80
3.2.1 Problem 1 80
3.2.1.1 Limiting Case 81
3.2.2 Problem 2 83
3.2.3 Problem 3 85
3.3 Measure of Robust Performance 85
3.4 Design Procedure 86
3.4.1 Tuning Rule 86
3.4.2 Simple Method to Calculate Kc,Min 87
3.5 Simulation Studies 88
3.5.1 Example 1 88
3.5.1.1 Effect of Measurement Noise 90
3.5.2 Example 2 91
3.5.3 Example 3 92
3.5.4 Example 4: Unstable Nonlinear Bioreactor 95
3.5.5 Effect of Noise on Relay Output 99
3.6 Conclusions 99
References 100
4 Decentralized PID Controllers for Stable Systems 101
4.1 Introduction 101
4.2 Design Procedure 103
4.3 Simulation Studies on Stable Systems 104
4.3.1 Example 1 104
4.3.1.1 The Effect of Measurement Noise on Stable System 107
4.3.2 Example 2 110
4.3.3 Example 3 112
4.3.4 Example 4 115
4.4 Conclusions 117
References 118
5 Decentralized PID Controllers for Unstable Systems 119
5.1 Introduction 119
5.2 Design Procedure 120
5.3 Simulation Studies of Unstable Systems 121
5.3.1 Example 1 121
5.3.1.1 Calculation of Kc,Min 122
5.3.1.2 Calculation of Kc,max 122
5.3.2 Example 2 127
5.3.2.1 Calculation of Kc,min 127
5.3.2.2 Calculation of Kc,max 128
5.3.3 Example 3 131
5.3.3.1 Calculation of Kc,min 131
5.3.3.2 Calculation of Kc,max 131
5.4 Conclusion 136
References 136
6 Centralized PID Controllers for Unstable System 138
6.1 Introduction 138
6.2 Controllers Design 139
6.3 Robustness Analysis 141
6.4 Simulations Studies on Unstable Systems 142
6.4.1 Example 1 142
6.4.2 Example 2 146
6.5 Conclusions 150
References 151
7 Refined Ziegler–Nichols Tuning Method for Unstable SISO Systems 152
7.1 Introduction 152
7.2 Controller Design Method 153
7.3 Simulation Studies 154
7.3.1 Example 1 154
7.3.2 Example 2 156
7.3.3 Example 3 160
7.3.4 Example 4 163
7.3.5 Example 5 166
7.4 Improved Relay Tuning Method 169
7.5 Comparison With the Recent Method 173
7.6 Conclusions 174
References 174
8 Tuning Rules for PID Controllers for Unstable Systems 176
8.1 Controller Design Method for Unstable FOPTD System Based on System Parameters 176
8.1.1 Example 1 180
8.2 Controller Design for Unstable System Based on Ultimate Values 180
8.2.1 Case 1 182
8.2.2 Comparison with Other Methods 184
8.3 Conclusions 190
References 190
9 Auto-tuning of Decentralized Unstable System With Refined ZN Method 191
9.1 Introduction 191
9.2 Controllers Design 191
9.3 Simulation Studies 194
9.3.1 Example 1 194
9.3.2 Example 2 200
9.4 Conclusions 205
Reference 206
Appendix A 207
Appendix B 209
Improved Continuous Cycling Method for Stable FOPTD System 209
Appendix C 216
CODE 1: MATLAB Code for Determining the Minimum and Maximum Value of Controller Gain 216
CODE II: MATLAB Code for Determining the Updated Minimum and Maximum Value of Controller Gain 218
Appendix D 219
Simulink Diagrams 219
Index 222