The primary purpose of control is to force desired behavior in an unpredictable environment, under the actions of unknown, possibly unmeasurable disturbances and unpredictable, and therefore probably nonzero, initial conditions. This means that tracking and tracking control synthesis are fundamental control issues. Surprisingly, however, tracking theory has not been well developed, and stability theory has dominated. Tracking Control of Linear Systems presents the fundamentals of tracking theory for control systems. The book introduces the full transfer function matrix F(s), which substantially changes the theory of linear dynamical and control systems and enables a novel synthesis of tracking control that works more effectively in real environments. An Introduction to the New Fundamentals of the Theory of Linear Control Systems The book begins by re-examining classic linear control systems theory. It then defines and determines the system full (complete) transfer function matrix F(s) for two classes of systems: input-output (IO) control systems and input-state-output (ISO) control systems. The book also discusses the fundamentals of tracking and trackability. It presents new Lyapunov tracking control algorithms and natural tracking control (NTC) algorithms, which ensure the quality of the tracking under arbitrary disturbances and initial conditions. This natural tracking control is robust, adaptable, and simple to implement. Advances in Linear Control Systems Theory: Tracking and Trackability This book familiarizes readers with novel, sophisticated approaches and methods for tracking control design in real conditions. Contributing to the advancement of linear control systems theory, this work opens new directions for research in time-invariant continuous-time linear control systems. It builds on previous works in the field, extending treatment of the system transfer functions, stability issues, the plant–control relationship, and control synthesis.
Author(s): Lyubomir T. Gruyitch
Publisher: CRC Press
Year: 2013
Language: English
Pages: xviii+405
Tracking Control of Linear Systems......Page 4
Contents......Page 6
List of Figures......Page 12
Acknowledgments......Page 14
0.1 On the book......Page 16
0.2 In gratitude......Page 19
Part I: On Control Systems Classic Fundamentals......Page 20
1.1 Time, physical variables and systems......Page 22
1.2 Systems and complex domain......Page 26
1.3 Notational preliminaries......Page 33
2.1.1 General IO system description......Page 36
2.1.2 Input-output (IO) description of a plant......Page 45
2.1.3 Input-output (IO) description of a feedback con-troller......Page 46
2.2.1 General ISO system......Page 47
2.2.2 ISO plant......Page 48
2.2.3 ISO feedback controller......Page 49
2.2.4 ISO feedback control system......Page 50
3.1 System regime meaning......Page 52
3.2.1 Introduction......Page 53
3.3.1 Introduction......Page 54
3.3.2 IO control systems......Page 58
3.3.3 ISO control systems......Page 62
4.1 On definitions of G(s)......Page 72
4.2 On importance of G(s)......Page 73
Part II: Novel System Fundamental: Full transfer Function Matrix F(s)......Page 76
5 Problem statement......Page 78
6.1 Nondegenerate and degenerate matrices......Page 80
6.2 Basic lemma......Page 84
7.1.1 Definition of F(s): IO system......Page 86
7.1.2 Definition of F(s): ISO system......Page 89
7.2 Determination of F(s) in genera......Page 92
7.2.1 F(s) of the IO system......Page 93
7.2.2 F(s) of the ISO system......Page 103
7.3.1 F(s) of the IO plant......Page 115
7.3.2 F(s) of the IO controller......Page 117
7.3.3 F(s) of the IO control system......Page 118
7.4.1 F(s) of the ISO plant......Page 122
7.4.2 F(s) of the ISO controller......Page 124
7.4.3 F(s) of the ISO control system......Page 125
7.5 Conclusion: general form of F(s)......Page 129
7.6.1 The IO system......Page 130
7.6.2 The ISO system......Page 133
Part III: Novel Control Theories: Tracking And Trackability......Page 136
8.1 Tracking generally......Page 138
8.2 Tracking versus stability......Page 141
8.3.1 On perfect tracking generally......Page 143
8.3.2 The IO systems......Page 145
8.3.3 The ISO systems......Page 149
8.4.1 Output space: tracking in Lyapunov sense......Page 152
8.4.2 Output space: tracking with FRT......Page 157
8.4.3 Internal dynamics space: the IO plant tracking......Page 162
8.4.4 The ISO plant tracking in Lyapunov sense......Page 170
8.4.5 State space: the ISO plant tracking with FRT......Page 173
8.4.6 Tracking of the ISO plant and the target set......Page 177
9.1 Trackability versus controllability......Page 188
9.2.1 Perfect trackability......Page 190
9.2.2 Perfect natural trackability......Page 193
9.2.3 Imperfect trackability......Page 194
9.2.4 Imperfect natural trackability......Page 197
9.2.5 Imperfect elementwise trackability......Page 200
9.3.1 IO plant perfect (natural) trackability......Page 204
9.3.2 ISO plant perfect (natural) trackability......Page 210
9.4.1 IO plant imperfect (natural) trackability......Page 216
9.4.2 ISO plant imperfect (natural) trackability......Page 220
Part IV: Novel Tracking Control Synthesis......Page 226
10.1 Generating theorem......Page 228
10.2 LITC of the IO plants......Page 234
10.3 LITC of the ISO plants......Page 237
11.1.2 Definitions of VLF's......Page 242
11.1.3 VLF generalization of the classical stability theo-rems......Page 244
11.1.4 VLF forms......Page 245
11.2.1 Arbitrary scalar Lyapunov function......Page 247
11.2.2 The first choice of a scalar Lyapunov function......Page 251
11.2.3 The second choice of a scalar Lyapunov function......Page 254
11.2.4 Choice of a vector Lyapunov function......Page 258
11.3.1 Arbitrary scalar Lyapunov function......Page 261
11.3.2 Choice of a scalar Lyapunov function......Page 264
11.3.3 Choice of a vector Lyapunov function......Page 266
12.1 Concept of NTC......Page 268
12.2.1 General consideration......Page 286
12.2.2 Control synthesis for specific tracking qualities......Page 290
12.3.1 General consideration......Page 298
12.3.2 Control synthesis for specific tracking qualities......Page 305
13.1 General consideration......Page 312
13.2 The IO plant......Page 315
13.3 The ISO plant......Page 317
Part V: Conclusion......Page 320
14 On F(s)......Page 322
15 On tracking and trackability......Page 324
16 On tracking control......Page 326
17 Recommendation......Page 328
Bibliography......Page 330
Part VI: Appendixes......Page 358
A.1 Abbreviations......Page 360
A.3.1 Calligraphic Letters......Page 361
A.3.2 Fraktur Letters......Page 362
A.3.3 Greek Letters......Page 365
A.3.4 Roman Letters......Page 368
A.4.1 Names......Page 376
A.4.2 Symbols And Vectors......Page 377
A.5 Units......Page 380
Appendix B: From IO system to ISO system......Page 382
Appendix C: From ISO system to IO system......Page 386
Appendix D: Proof of Theorem 64......Page 388
Appendix E: Proof of Theorem 67......Page 390
Appendix F: Proof of Theorem 72......Page 396
Appendix G: Proof of Theorem 91......Page 398
Appendix H: Proof of Lemma 102 (Basic Lemma)......Page 400
Appendix I: Proof of Theorem 116......Page 402
Appendix J: Proof of Theorem 142......Page 406
Appendix K: Proof of Theorem 145......Page 408
Appendix L: Proof of Theorem 149......Page 410
Author Index......Page 412
Subject Index......Page 414
