Discrete-time control systems = 离散时间控制系统 / 2nd ed.

preface iii

chapter 1

introduction to discrete-tim control systems

1-1 introduction, 1

1-2 digital control systems, 5

1-3 quantizing and quantization error, 8

1-4 data acquisition, conversion, and distribution systems, 11

1-5 concluding comments, 20

chapter 2

the z transform 23

2-1 introduction, 23

2-2 the z transform, 24

2-3 z transforms of elementary functions, 25

2-4 important properties and theorems of the z transform, 31

2-5 the inverse z transform, 37

2-6 z transform method for solving difference equations, 52

2-7 concluding comments, 54

example problems and solutions, 55

problems, 70

chapter 3

.z-plane analysis of discrete. time control systems 74

3-1 introduction, 74

3-2 impulse sampling and data hold, 75

3-3 obtaining the ztransform by the convolution integral method, 83

3-4 reconstructing original signals from sampled signals, 90

3-5 the pulse transfer function, 98

3-6 realization of digital controllers and digital filters, 122

example problems and solutions, 138

problems, 166

chapter 4

design of discrete-time control systems by conventional methods 173

4-1 introduction, 173

4-2 mapping between the s plane and the z plane, 174

4-3 stability analysis of closed-loop systems in the z plane, 182

4-4 transient and steady-state response analysis, 193

4-5 design based on the root-locus method, 204

4-6 design based on the frequency-response method, 225

4-7 analytical design method, 242

example problems and solutions, 257

problems, 288

chapter 5

state-space analysis 293

5-1 introduction, 293

5-2 state-space representations of discrete-time systems, 297

5-3 solving discrete-time state-space equations, 302

5-4 pulse-transfer-function matrix, 310

5-5 discretization of continuous-time state-space equations, 312

5-6 liapunov stability analysis, 321

example problems and solutions, 336

problems, 370

chapter 6

pole placement and observer design 377

6-1 introduction, 377

6-2 controllability, 379

6-3 observability, 388

6-4 useful transformations in state-space analysis and design, 396

6-5 design via pole placement, 402

6-6 state observers, 421

6-7 servo systems, 460

example problems and solutions, 474

problems, 510

chapter 7

polynomial equations approach to control systems design 517

7-1 introduction, 517

7-2 diophantine equation, 518

7-3 illustrative example, 522

7-4 polynomial equations approach to control systems design, 525

7-5 design of model matching control systems, 532

example problems and solutions, 540

problems, 562

chapter 8

quadratic optimal control systems 566

8-1 introduction, 566

8-2 quadratic optimal control, 569

8-3 steady-state quadratic optimal control, 587

8-4 quadratic optimal control of a servo system, 596

example problems and solutions, 609

problems, 629

appendix a

vector-matrix analysis 633

a-1 definitions, 633

a-2 determinants, 633

a-3 inversion of matrices, 635

a-4 rules of matrix operations, 637

a-5 vectors and vector analysis, 643

a-6 eigenvalues, eigenvectors, and similarity transformation, 649

a-7 quadratic forms, 659

a-8 pseudoinverses, 663

example problems and solutions, 666

appendix b

z transform theory 681

b-1 introduction, 681

b-2 useful theorems of the z transform theory, 681

b-3 inverse z transformation and inversion integral method, 686

b-4 modified z transform method, 691

example problems and solutions, 697

appendix c

pole placement design with vector control 704

c-1 introduction, 704

c-2 preliminary discussions, 704

c-3 pole placement design, 707

example problems and solutions, 718

references 730

index 735