Multivariable Feedback Control

Professor Sigurd Skogestad, Norwegian University of Science and Technology (NTNU)Head of the Department of Chemical Engineering. Author of more than 100 journal publications and 150 conference publications. He was awarded "Innstilling to the King" for his Siv.Ing. degree in 1979, a Fullbright fellowship in 1983, received the Ted Peterson Award from AIChE in 1989, the George S. Axelby Outstanding Paper Award from IEEE in 1990, and the O. Hugo Schuck Best Paper Award from the American Automatic Control Council in 1992. Professor Ian Postlethwaite, University of Leicester, UKHead of Engineering Department, Fellow of the Institute of Electrical and Electronics Engineers, Fellow of the Institution of Electrical Engineers, and a Fellow of the Institute of Measurement and Control. In 1991 he received the IEE FC Williams Premium, in 2001 the Sir Harold Hartley Medal of the InstMC and in 2002 the Best Paper Prize for an article published in the IFAC Journal of Control Engineering Practice over the period 1999-2002.

• Preface xi1 Introduction 11.1 The process of control system design 11.2 The control problem 21.3 Transfer functions 31.4 Scaling 51.5 Deriving linear models 71.6 Notation 102 Classical Feedback Control 152.1 Frequency response 152.2 Feedback control 202.3 Closed-loop stability 262.4 Evaluating closed-loop performance 282.5 Controller design 402.6 Loop shaping 422.7 IMC design procedure and PID control for stable plants 542.8 Shaping closed-loop transfer functions 592.9 Conclusion 653 Introduction To Multivariable Control 673.1 Introduction 673.2 Transfer functions for MIMO systems 683.3 Multivariable frequency response analysis 713.4 Relative gain array (RGA) 823.5 Control of multivariable plants 913.6 Introduction to multivariable RHP-zeros 953.7 Introduction to MIMO robustness 983.8 General control problem formulation 1043.9 Additional exercises 1153.10 Conclusion 1174 Elements of Linear System Theory 1194.1 System descriptions 1194.2 State controllability and state observability 1274.3 Stability 1344.4 Poles 1354.5 Zeros 1384.6 Some important remarks on poles and zeros 1414.7 Internal stability of feedback systems 1444.8 Stabilizing controllers 1484.9 Stability analysis in the frequency domain 1504.10 System norms 1564.11 Conclusion 1625 Limitations On Performance In Siso Systems 1635.1 Input-output controllability 1635.2 Fundamental limitations on sensitivity 1675.3 Fundamental limitations: bounds on peaks 1725.4 Perfect control and plant inversion 1805.5 Ideal ISE optimal control 1815.6 Limitations imposed by time delays 1825.7 Limitations imposed by RHP-zeros 1835.8 Limitations imposed by phase lag 1915.9 Limitations imposed by unstable (RHP) poles 1925.10 Performance requirements imposed by disturbances and commands 1985.11 Limitations imposed by input constraints 1995.12 Limitations imposed by uncertainly 2035.13 Summary: controllability analysis with feedback control 2065.14 Summary: controllability analysis with feedforward control 2095.15 Applications of controllability analysis 2105.16 Conclusion 2196 Limitations On Performance In Mimo Systems 2216.1 Introduction 2216.2 Fundamental limitations an sensitivity 2226.3 Fundamental limitations: bounds on peaks 2236.4 Functional controllability 2326.5 Limitations imposed by time delays 2336.6 Limitations imposed by RHP-zeros 2356.7 Limitations imposed by unstable (RHP) poles 2386.8 Performance requirements imposed by disturbances 2386.9 Limitations imposed by input constraints 2406.10 Limitations imposed by uncertainty 2426.11 MIMO input-output controllability 2536.12 Conclusion 258.7 Uncertainty and Robustness For Siso Systems 2597.1 Introduction to robustness 2597.2 Representing uncertainty 2607.3 Parametric uncertainty 2627.4 Representing uncertainty in the frequency domain 2657.5 SISO robust stability 2747.6 SISO robust performance 2817.7 Additional exorcises 2877.8 Conclusion 2888 Robust Stability and Performance Analysis For Mimo Systems 2898.1 General control configuration with uncertainly 2898.2 Representing uncertainty 2908.3 Obtaining P, N and M 2988.4 Definitions of robust stability and robust performance 2998.5 Robust stability of the M Δ-structure 3018.6 Robust stability for complex unstructured uncertainty 3028.7 Robust stability with structured uncertainly: motivation 3058.8 The structured singular value 3068.9 Robust stability with structured uncertainly 3138.10 Robust, performance 3168.11 Application: robust performance with input uncertainty 3208.12 μ-synthesis and DK-iteration 3288.13 Further remarks on μ 3368.14 Conclusion 3389 Controller Design 3419.1 Trade-offs in MIMO feedback design 3419.2 LQG control 3449.3 ℋ2 and ℋ∞ control 3529.4 ℋ∞ loop-shaping design 3649.5 Conclusion 38110 Control Structure Design 38310.1 Introduction 38310.2 Optimal operation and control 38510.3 Selection of primary controlled outputs 38810.4 Regulatory control layer 40310.5 Control configuration elements 41910.6 Decentralized feedback control 42810.7 Conclusion 45311 Model Reduction 45511.1 Introduction 45511.2 Truncation and residualization 45611.3 Balanced realizations 45711.4 Balanced truncation and balanced residualization 45811.5 Optimal Hankel norm approximation 45911.6 Reduction of unstable models 46211.7 Model reduction using Matlab 46211.8 Two practical examples 46311.9 Conclusion 47112 Linear Matrix Inequalities 47312.1 Introduction to LMI problems 47312.2 Types of LMI problems 47612.3 Tricks in LMT problems 47912.4 Case study: anti-windup compensator synthesis 48412.5 Conclusion 49013 Case Studies 49113.1 Introduction 49113.2 Helicopter control 49213.3 Aero-engine control 50013.4 Distillation process 50913.5 Conclusion 514A Matrix Theory and Norms 515A.1 Basics 515A.2 Eigenvalues and eigenvectors 51 8A.3 Singular value decomposition 520A.4 Relative gain array 526A.5 Norms 530A.6 All-pass factorization of transfer function matrices 541A.7 Factorization of the sensitivity function 542A.8 Linear fractional transformations 543B Project Work and Sample Exam 547B.1 Project work 547B.2 Sample exam 548Bibliography 553Index 563