Table of Contents
Chapter 1 Introduction to Digital Control 1
1.1 Why Digital Control? 2
1.2 The Structure of a Digital Control System 2
1.3 Examples of Digital Control Systems 3
Resources 6
Problems 7
Chapter 2 Discrete-Time Systems 9
2.1 Analog Systems with Piecewise Constant Inputs 9
2.2 Difference Equations 11
2.3 The z-Transform 12
2.4 Computer-Aided Design 31
2.5 z-Transform Solution of Difference Equations 32
2.6 The Time Response of a Discrete-Time System 33
2.7 The Modified z-Transform 38
2.8 Frequency Response of Discrete-Time Systems 40
2.9 The Sampling Theorem 46
Resources 50
Problems 51
Computer Exercises 53
Chapter 3 Modeling of Digital Control Systems 55
3.1 ADC Model 55
3.2 DAC Model 56
3.3 The Transfer Function of the ZOH 57
3.4 Effect of Sampler on Transfer Function of a Cascade 58
3.5 Transfer Function for the DAC, Analog Subsystem, ADC Combination 62
3.6 Systems with Transport Lag 70
3.7 The Closed-Loop Transport Function 72
3.8 Analog Disturbances in a Digital System 75
3.9 Steady-State Error and Error Constants 77
3.10 MATLAB Commands 80
Resources 81
Problems 82
Computer Exercises 85
Chapter 4 Stability of Digital Control Systems 87
4.1 Definitions of Stability 87
4.2 Stable z-Domain Pole Locations 89
4.3 Stability Conditions 89
4.4 Stability Determination 97
4.5 Jury Test 100
4.6 Nyquist Criterion 104
Resources 118
Problems 118
Computer Exercises 120
Chapter 5 Analog Control System Design 123
5.1 The Root Locus 123
5.2 Root Locus Using MATLAB 128
5.3 Design Specifications and the Effect of Gain Variation 128
5.4 Root Locus Design 131
5.5 Empirical Tuning of PID Controllers 154
Resources158
Problems 158
Computer Exercises 159
Chapter 6 Digital Control System Design 161
6.1 z-Domain Root Locus 161
6.2 z-Domain Digital Control System Design 164
6.3 Digital Implementation of Analog Controller Design 176
6.4 Direct z-Domain Digital Controller Design 196
6.5 Frequency Response Design 202
6.6 Direct Control Design 210
6.7 Finite Settling Time Design 215
Resources 225
Problems 225
Computer Exercises 227
Chapter 7 State-Space Representation 229
7.1 State Variables 229
7.2 State-Space Representation 232
7.3 Linearization of Nonlinear State Equations 237
7.4 The Solution of Linear State-Space Equations 240
7.5 The Transfer Function Matrix 256
7.6 Discrete-Time State-Space Equations 258
7.7 Solution of Discrete-Time State-Space Equations 261
7.8 z-Transfer Function from State-Space Equations 268
7.9 Similarity Transformation 270
Resources 274
Problems 275
Computer Exercises 279
Chapter 8 Properties of State-Space Models 281
8.1 Stability of State-Space Realizations 282
8.2 Controllability and Stabilizability 290
8.3 Observability and Detectability 301
8.4 Poles and Zeros of Multivariable Systems 307
8.5 State-Space Realizations 313
8.6 Duality 326
Resources 327
Problems 328
Computer Exercises 333
Chapter 9 State Feedback Control 335
9.1 On State and Output Feedback 335
9.2 Pole Placement 337
9.3 Servo Problem 349
9.4 Invariance of System Zeros 353
9.5 State Estimation 355
9.6 Observer State Feedback 362
9.7 Pole Assignment Using Transfer Functions 370
Resources 374
Problems 374
Computer Exercises 378
Chapter 10 Optimal Control 379
10.1 Optimization 379
10.2 Optimal Control 384
10.3 The Linear Quadratic Regulator 389
10.4 Steady-State Quadratic Regulator 399
10.5 Hamiltonian System 406
Resources 409
Problems 410
Computer Exercises 413
Chapter 11 Elements of Nonlinear Digital Control Systems 415
11.1 Discretization of Nonlinear Systems 415
11.2 Nonlinear Difference Equations 424
11.3 Equilibrium of Nonlinear Discrete-Time System 425
11.4 Lyapunov Stability Theory 426
11.5 Stability of Analog Systems with Digital Control 439
11.6 State Plane Analysis 442
11.7 Discrete-Time Nonlinear Controller Design 447
Resources 452
Problems 452
Computer Exercises 455
Chapter 12 Practical Issues 457
12.1 Design of the Hardware and Software Architecture 457
12.2 Choice of the Sampling Period 461
12.3 Controller Structure 468
12.4 PID Control 471
12.5 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
