Robust Control Design with MATLAB®

Robust Control Design with MATLAB® (second edition) helps the student to learn how to use well-developed advanced robust control design methods in practical cases. To this end, several realistic control design examples from teaching-laboratory experiments, such as a two-wheeled, self-balancing robot, to complex systems like a flexible-link manipulator are given detailed presentation. All of these exercises are conducted using MATLAB® Robust Control Toolbox 3, Control System Toolbox and Simulink®. By sharing their experiences in industrial cases with minimum recourse to complicated theories and formulae, the authors convey essential ideas and useful insights into robust industrial control systems design using major H-infinity optimization and related methods allowing readers quickly to move on with their own challenges. The hands-on tutorial style of this text rests on an abundance of examples and features for the second edition: • rewritten and simplified presentation of theoretical and methodological material including original coverage of linear matrix inequalities; • new Part II forming a tutorial on Robust Control Toolbox 3; • fresh design problems including the control of a two-rotor dynamic system; and • end-of-chapter exercises. Electronic supplements to the written text that can be downloaded from extras.springer.com/isbn include: • M-files developed with MATLAB® help in understanding the essence of robust control system design portrayed in text-based examples; • MDL-files for simulation of open- and closed-loop systems in Simulink®; and • a solutions manual available free of charge to those adopting Robust Control Design with MATLAB® as a textbook for courses. Robust Control Design with MATLAB® is for graduate students and practising engineers who want to learn how to deal with robust control design problems without spending a lot of time in researching complex theoretical developments. Table of Contents Cover Robust Control Design with MATLAB, Second Edition ISBN 9781447146810 ISBN 9781447146827 Series Editors' Foreword Preface to the Second Edition Preface to the First Edition Contents Part I Basic Methods and Theory Chapter 1 Introduction 1.1 Control-System Representations 1.2 System Stabilities 1.3 Coprime Factorization and Stabilizing Controllers 1.4 Signals and System Norms o 1.4.1 Vector Norms and Signal Norms o 1.4.2 System Norms Chapter 2 Modeling of Uncertain Systems 2.1 Unstructured Uncertainties 2.2 Parametric Uncertainty 2.3 Linear Fractional Transformations 2.4 Structured Uncertainties Chapter 3 Robust Design Specification 3.1 Small-Gain Theorem and Robust Stabilization 3.2 Performance Considerations 3.3 Structured Singular Values Chapter 4 H-infinity Design 4.1 Mixed Sensitivity H-infinity Optimization 4.2 2-Degree-of-Freedom H-infinity Design 4.3 H-infinity Suboptimal Solutions o 4.3.1 Solution Formulas for Normalized Systems o 4.3.2 Solution to S-over-KS Design o 4.3.3 The Case of D22 = 0 o 4.3.4 Normalization Transformations o 4.3.5 Direct Formulas for H-infinity Suboptimal Central Controller 4.4 Formulas for Discrete-Time Cases Chapter 5 H-infinity Loop-Shaping Design Procedures 5.1 Robust Stabilization Against Normalized Coprime Factor Perturbations 5.2 Loop-Shaping Design Procedures 5.3 Formulas for the Discrete-Time Case o 5.3.1 Normalized Coprime Factorization of Discrete-Time Plant o 5.3.2 Robust Controller Formulas o 5.3.3 The Strictly Proper Case o 5.3.4 On the Three DARE Solutions 5.4 A Mixed Optimization Design Method with LSDP Chapter 6 �-Analysis and Synthesis 6.1 Consideration of Robust Performance 6.2 �-Synthesis: D-K Iteration Method 6.3 �-Synthesis: �-K Iteration Method Chapter 7 Lower-Order Controllers 7.1 Absolute-Error Approximation Methods o 7.1.1 Balanced Truncation Method o 7.1.2 Singular Perturbation Approximation o 7.1.3 Hankel-Norm Approximation 7.2 Reduction via Fractional Factors o 7.2.1 Fractional Balanced Truncation (FBT) Method o 7.2.2 Fractional Singular Perturbation Approximation (FSPA) Method 7.3 Relative-Error Approximation Methods 7.4 Frequency-Weighted Approximation Methods o 7.4.1 Frequency-Weighted Balanced Truncation (FWBT) o 7.4.2 Frequency-Weighted Singular Perturbation Approximation (FWSPA) o 7.4.3 Frequency-Weighted Moduli Truncation Method (FWMT) Chapter 8 LMI Approach 8.1 Basics About LMI 8.2 Control Problems Using LMI o 8.2.1 Lyapunov Stability Criterion o 8.2.2 Stabilization by State Feedback o 8.2.3 Computation of L2 Norm o 8.2.4 Computation of H-infinity Norm o 8.2.5 Formulation of LQR in LMI 8.3 A Few More Properties Concerning LMI o 8.3.1 Congruence Transformation o 8.3.2 Schur Complements for Nonstrict Inequalities o 8.3.3 Projection and Finsler's Lemmas o 8.3.4 The S-Procedure for Quadratic Functions o 8.3.5 Dualization Lemma Part II Introduction to Robust Control Toolbox v3 Chapter 9 Building Uncertain Models 9.1 LTI Models 9.2 Structured Uncertainty Models o 9.2.1 Uncertain Real Parameters o 9.2.2 Uncertain State-Space Systems o 9.2.3 Properties of Uncertain Systems o 9.2.4 Other Functions to Build Uncertain Models o 9.2.5 Decomposing Uncertain Objects 9.3 Building Uncertain Models Using iconnect and sysic 9.4 Unstructured Uncertainty Models o 9.4.1 Models with Additive Uncertainty o 9.4.2 Models with Multiplicative Uncertainty o 9.4.3 Unmodeled Dynamics o 9.4.4 Multivariable Plants with Unstructured Uncertainty 9.5 Exercises Chapter 10 Robust Stability and Performance 10.1 Robust Stability Analysis 10.2 Robust Performance Analysis 10.3 Worst-Case Gain 10.4 Exercises Chapter 11 H-infinity Design 11.1 H-infinity Loop-Shaping Design 11.2 Mixed Sensitivity Design 11.3 Other Versions of H-infinity Design o 11.3.1 H-infinity Control with Models o 11.3.2 Two-Degree-of-Freedom H-infinity Control 11.4 Exercises Chapter 12 �-Synthesis 12.1 The �-Synthesis Problem 12.2 �-Synthesis by D-K Iterations 12.3 Versions of �-Synthesis o 12.3.1 �-Synthesis with Model o 12.3.2 �-Synthesis of 2-Degree-of-Freedom Controller 12.4 Practical Aspects of �-Analysis and �-Synthesis 12.5 Exercises Chapter 13 Analysis and Design of Parameter-Dependent Systems 13.1 Representation of Parameter-Dependent Systems o 13.1.1 SYSTEM Matrix o 13.1.2 Affine Parameter-Dependent Models o 13.1.3 Polytopic Models 13.2 Analysis of Parameter-Dependent Systems 13.3 Gain Scheduling Design for Parameter-Dependent Systems 13.4 Exercises Part III Design Examples Chapter 14 Robust Control of a Hard Disk Drive 14.1 Hard Disk Drive Servo System 14.2 Derivation of Uncertainty Model 14.3 Closed-Loop System Design Specification o 14.3.1 Nominal Performance o 14.3.2 Robust Stability o 14.3.3 Robust Performance 14.4 System Interconnections 14.5 Controller Design in Continuous-Time o 14.5.1 �-Design o 14.5.2 H-infinity Design o 14.5.3 H-infinity Loop-Shaping Design 14.6 Comparison of Designed Controllers 14.7 Controller-Order Reduction 14.8 Design of Discrete-Time Controller 14.9 Nonlinear System Simulation 14.10 Conclusions 14.11 Notes and References Chapter 15 A Triple Inverted Pendulum Control System Design 15.1 System Description 15.2 Modeling of Uncertainties 15.3 Design Specification o 15.3.1 Robust Stability o 15.3.2 Nominal Performance o 15.3.3 Robust Performance 15.4 System Interconnections 15.5 H-infinity Design 15.6 �-Synthesis 15.7 Nonlinear System Simulation 15.8 Conclusions 15.9 Notes and References Chapter 16 Robust Control of a Distillation Column 16.1 Introduction 16.2 Dynamic Model of the Distillation Column 16.3 Uncertainty Modeling 16.4 Closed-Loop System Performance Specification 16.5 Open-Loop and Closed-Loop System Interconnections 16.6 Controller Design o 16.6.1 Loop-Shaping Design o 16.6.2 �-Synthesis 16.7 Nonlinear System Simulation 16.8 Conclusions 16.9 Notes and References Chapter 17 Robust Control of a Flexible-Link Manipulator 17.1 Dynamic Model of the Flexible Manipulator 17.2 A Linear Model of the Uncertain System 17.3 System Performance Specification 17.4 System Interconnections 17.5 Controller Design and Analysis 17.6 Nonlinear System Simulations 17.7 Conclusions 17.8 Notes and References Chapter 18 Robust Control of a Twin-Rotor Aerodynamic System 18.1 Twin-Rotor Aerodynamic System 18.2 Nonlinear System Model 18.3 Linearized System Model 18.4 Uncertainty Modeling 18.5 Closed-Loop System Performance Requirements o 18.5.1 Robust Stability o 18.5.2 Nominal Performance o 18.5.3 Robust Performance 18.6 System Interconnections 18.7 �-Synthesis 18.8 Nonlinear System Simulation 18.9 Experimental Results 18.10 Conclusions o 18.10.1 Notes and References Chapter 19 Robust Control of Self-balancing Two-Wheeled Robot 19.1 Introduction 19.2 Uncertain Model of the Two-Wheeled Robot 19.3 Design of Robust Controller 19.4 Closed-Loop System Properties 19.5 Experimental Results 19.6 Conclusions 19.7 Notes and References References Index