MANFRED MORARI ROBUST PROCESS CONTROL EVANGHELOS ZAFIRIOU Morari M,Zafiriou E. New Jersey:Prentice-Hall,1989
Morari M, Zafiriou E. New Jersey: Prentice-Hall, 1989
Contents PREFACE XV NOMENCLATURE xix 1 INTRODUCTION 1 1.1 The Evolution of Control Theory .. 1 1.2 Controller Parametrization:The IMC Structure.. 3 1.3 Robustness 4 1.4 Scope of Book.···.·. 4 1.5 Some Hints for the Reader....... 5 Part I:CONTINUOUS SINGLE-INPUT SINGLE-OUTPUT SYSTEMS 9 2 FUNDAMENTALS OF SISO FEEDBACK CONTROL 11 2.1 Definitions..·.··,······ 11 2.2 Formulation of Control Problem 13 2.2.1 Process[odel..·.·.··· 14 2.2.2 Model Uncertainty Description 15 2.2.3 Input Specification.,····,··· 19 2.2.4 Control Objectives... 21 2.3 Internal Stability........... 22 2.4 Nominal Performance.... 23 2.4.1 Sensitivity and Complementary Sensitivity Function 24 2.4.2 Two-Degree-of-Freedom Controller ·· 25 2.4.3 Asymptotic Properties of the Closed-Loop Response (Sys- tem Type).,·,,, 27 2.4.4 Linear Quadratic (H2-)Optimal Control... 28 2.4.5 Ho-Optimal Control...... 29 2.5 Robust Stability 31 2.6 Robust Performance 3 2.6.1 H2 Performance Objective....... 34 2.6.2 Hoo Performance Objective 35
CONTENTS y 16.3.3 Controllers··········· ..,444 lG.4 Results for Operating Point A...,··.· 445 16.4.1 Discussion of Controllers..·,·,·· 446 16.4.2 Conclusions..... ...451 16.5 Effect of Nonlinearity (Results for Operating Point C) ·、···,.452 l6.5.1 odelling...·..,··,············· 452 453 16.5.2-Analysis.······· 16.5.3 Logarithmic Versus Unscaled Compositions..... 453 16.5.4 Transition from Operating Point A to C...... 455 456 l6.6 Conclusions,....,,····· 456 lG.7 References,.,·· 459 Appendix 469 References 479 Index
CONTENTS VI 2.7 Summary,······· 36 2.8 References..... 38 3 THE SISO IMC STRUCTURE FOR STABLE SYSTEMS 39 3.1 IMC Structure,.·....,,········,·········· 39 3.2 Stability Conditions for IMC·.··.:· 41 3.2.1 Internal Stability.....·.·.··· 41 3.2.2 Relationship with“Classic Feedback” 42 3.2.3 Implementation:Classic Feedback Versus IMC 44 3.3 Performance of IMC·.,·,················ 45 3.3.1 Sensitivity and Complementary Sensitivity Function 45 3.3.2 Two-Degree-of-Freedom Controller..... 46 3.3.3 Asymptotic Properties of Closed-Loop Response (System Type)·········: 46 3.3.4 The Concept of "Perfect Control" 47 3.4 Outline of the IMC Design Procedure... 50 3.4.1 Basic Design Philosophy.····· 50 3.4.2Two-Degree-of-Freedom Design.··, 52 3.4.3 Design in the Presence of Measurement Device Dynamics .54 3.5 Summary·,··········· 55 55 3.6 References.....,.·.·. I SISO IMC DESIGN FOR STABLE SYSTEMS 57 4.1 Nominal Performance........ 57 4.1.1 H2-Optimal Control.... 58 4.1.2 Design for Specific Input Forms.. 60 4.1.3 Minimum Error Norm for Step Inputs ..... 61 4.2 The IMC Filter.,·,,,··········,······ 64 4.2.1 Filter Form...· 64 4.2.2 A Qualitative Interpretation of the Function of the Filter 65 l.3 Robust Stability·,·..········ 66 4.3.1 Norm-Bounded Uncertainty Regions...... 66 4.3.2 General.Uncertainty Regions·..· 68 t.+Robust Performance·,..········· 70 4.4.1 Norm-Bounded Uncertainty Regions 70 +.4.2 General Uncertainty Regions··,·..···.· 73 1.5 Summary of IMC Design Procedure... 74 4.6 Application:IMC Design for a First-Order Deadtime System 75 4.6.1 Deadtime Uncertainty,...··..··.·,········ 75 4.6.2 Three-Parameter Uncertainty······ 81
vii CONTENTS 84 4.7 References...···· 85 5 SISO IMC DESIGN FOR UNSTABLE SYSTEMS 5.1 Parametrization of All Stabilizing Controllers...... 85 5.1.1 Conditions for Internal Stability 85 5.l.2 Controller parametrization.····· 87 5.2 Nominal Performance....,,······ 88 5.2.1H2-Optimal Controller.,.·:,,.··. 88 5.2.2 Design for Common Input Forms,····、·,·· 92 5.2.3 Minimum Error Norm for Step Inputs to Stable Systems.. 94 5.2.4Two-Degree-of-Freedom Controller··, 94 5.3 The IMC Filter·..··············· 96 5.3.1 Filter Form.··.,·· 96 5.3.2 Qualitative Interpretation of the Filter Function 99 5.4 Robust Stability....······ 101 5.4.1 Norm-Bounded Uncertainty Regions....... ...101 5.4.2 General Uncertainty Regions... .102 5.5 Robust Performance .. 102 5.6 Summary of the IMC Design Procedure 103 5.7 Applications,········· ..104 5.7.1 Distillation Column Base Level Control 104 5.7.2 NMP Unstable Systems..... 107 58 References.......·.···· ,.110 6 ISSUES IN SISO IMC DESIGN 113 6.1 Implications of IMC for Classic Feedback Controllers .··.113 6.l.1 General Relationships...,..·.,...·. 113 6.l.2 PID Settings for Simple Models..·..··· 114 6.1.3 PID Settings for a First-Order System with Deadtime ·.,121 6.1.4 Summary...·.········· ·········.125 6.2 IMC Interpretation of Smith Predictor Controller..........126 6.2.1 General Relationships ....126 6.2.2 Some Myths about the Tuning of Smith-Predictor Controllers128 6.2.3 Robust Tuning of Smith-Predictor Controller for First- Order System with Deadtime.,·.··...·....,..l30 6.2.4 Summary··········· 131 6.3 Feedforward Control....... 131 6.3.1 Objectives and Structure 131 6.3.2 Design.······ 132 6.3.3 Summary..... ,,135