Digital Control Engineering Analysis and Design

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1 Digital Control Engineering Analysis and Design M. Sami Fadali Antonio Visioli AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is an imprint of Elsevier

2 Contents CHAPTER 1 Introduction to Digital Control Why Digital Control? The Structure of a Digital Control System Examples of Digital Control Systems 3 Resources 6 Problems 7 CHAPTER 2 Discrete-Time Systems Analog Systems with Piecewise Constant Inputs Difference Equations The z-transform Computer-Aided Design z-transform Solution of Difference Equations The Time Response of a Discrete-Time System The Modified z-transform Frequency Response of Discrete-Time Systems The Sampling Theorem 46 Resources 50 Problems 51 Computer Exercises 53 CHAPTER 3 Modeling of Digital Control Systems ADC Model DAC Model The Transfer Function of the ZOH Effect of Sampler on Transfer Function of a Cascade Transfer Function for the DAC, Analog Subsystem, ADC Combination Systems with Transport Lag The Closed-Loop Transfer Function Analog Disturbances in a Digital System Steady-State Error and Error Constants 77

3 vi Contents 3.10 MATLAB Commands 80 Resources 81 Problems 82 Computer Exercises 85 CHAPTER 4 Stability of Digital Control Systems Definitions of Stability Stable z-domain Pole Locations Stability Conditions Stability Determination Jury Test Nyquist Criterion 104 Resources 118 Problems 118 Computer Exercises 120 CHAPTER 5 Analog Control System Design The Root Locus Root Locus Using MATLAB Design Specifications and the Effect of Gain Variation Root Locus Design Empirical Tuning of PID Controllers 154 Resources 158 Problems 158 Computer Exercises 159 CHAPTER 6 Digital Control System Design z-domain Root Locus z-domain Digital Control System Design Digital Implementation of Analog Controller Design Direct z-domain Digital Controller Design Frequency Response Design Direct Control Design Finite Settling Time Design 215 Resources 225 Problems 225 Computer Exercises 227 CHAPTER 7 State-Space Representation State Variables State-Space Representation Linearization of Nonlinear State Equations 237

4 Contents vii 7.4 The Solution of Linear State-Space Equations The Transfer Function Matrix Discrete-Time State-Space Equations Solution of Discrete-Time State-Space Equations z-transfer Function from State-Space Equations Similarity Transformation 270 Resources 274 Problems 275 Computer Exercises 279 CHAPTER 8 Properties of State-Space Models 28i 8.1 Stability of State-Space Realizations Controllability and Stabilizability Observability and Detectability Poles and Zeros of Multivariable Systems State-Space Realizations Duality 326 Resources 327 Problems 328 Computer Exercises 333 CHAPTER 9 State Feedback Control On State and Output Feedback Pole Placement Servo Problem Invariance of System Zeros State Estimation Observer State Feedback Pole Assignment Using Transfer Functions 370 Resources 374 Problems 374 Computer Exercises 378 CHAPTER 10 Optimal Control Optimization Optimal Control The Linear Quadratic Regulator Steady-State Quadratic Regulator Hamiltonian System 406 Resources 409 Problems 410 Computer Exercises 413

5 viii Contents CHAPTER 11 Elements of Nonlinear Digital Control Systems Discretization of Nonlinear Systems Nonlinear Difference Equations Equilibrium of Nonlinear Discrete-Time System Lyapunov Stability Theory Stability of Analog Systems with Digital Control State Plane Analysis Discrete-Time Nonlinear Controller Design 447 Resources 452 Problems 452 Computer Exercises 455 CHAPTER 12 Practical Issues Design of the Hardware and Software Architecture Choice of the Sampling Period Controller Structure PID Control Sampling Period Switching 481 Resources 494 Problems 494 Computer Exercises 495 APPENDIX I Table of Laplace and Z-Transforms 497 APPENDIX II Properties of the Z-Transform 499 APPENDIX III Review of Linear Algebra 501 A.1 Matrices 501 A.2 Equality of Matrices 502 A.3 Matrix Arithmetic 502 A.4 Determinant of a Matrix 508 A.5 Inverse of a Matrix 509 A.6 Eigenvalues 512 A.7 Eigenvectors 513 A.8 Norm of a Vector 516 A.9 Matrix Norms 517 A.10 Quadratic Forms 518 A.11 Matrix Differentiation/Integration 520 A.12 Kronecker Product 522 Resources 523 Index 525

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