book

Tracking Control of Linear Systems

Name: Tracking Control of Linear Systems
Author: Lyubomir T. Gruyitch
ISBN: 9781351831642

by Lyubomir T. Gruyitch

October 2018

Intermediate to advanced

423 pages

8h 42m

English

CRC Press

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Cover Page
Half Title Page
Title Page
Copyright
Contents
List of Figures
Acknowledgments
Preface
0.1 On the book0.2 In gratitude
I ON CONTROL SYSTEMS CLASSIC FUNDAMENTALS
1 Introduction
1.1 Time, physical variables and systems1.2 Systems and complex domain1.3 Notational preliminaries

2 Control Systems
2.1 IO control systems2.1.1 General IO system description2.1.2 Input-output (IO) description of a plant2.1.3 Input-output (IO) description of a feedback controller2.1.4 Input-output (IO) description of a feedback control system2.2 ISO control systems2.2.1 General ISO system2.2.2 ISO plant2.2.3 ISO feedback controller2.2.4 ISO feedback control system
3 System Regimes
3.1 System regime meaning3.2 Forced and free regimes3.2.1 Introduction3.2.2 Basic problem3.3 Desired regime3.3.1 Introduction3.3.2 IO control systems3.3.3 ISO control systems
4 Transfer function matrix G(s)
4.1 On definitions of G (s)4.2 On importance of G(s)
II NOVEL SYSTEM FUNDAMENTAL: FULL TRANSFER FUNCTION MATRIX F (s)
5 Problem statement
6 Nondegenerate matrices
6.1 Nondegenerate and degenerate matrices6.2 Basic lemma
7 Full transfer function matrix F(s)
7.1 General definitions of F(S)7.1.1 Definition of F(s): IO system7.1.2 Definition of F(s): ISO system7.2 Determination of F(s) in general7.2.1 F(s) of the IO system7.2.2 F(s) of the ISO system7.3 F(s) of the IO control system7.3.1 F(s) of the IO plant7.3.2 F(s) of the IO controller7.3.3 F(s) of the IO control system7.4 F(s) of the ISO control system7.4.1 F(s) of the ISO plant7.4.2 F(s) of the ISO controller7.4.3 F(s) of the ISO control system7.5 Conclusion: general form of F(s)7.6 Physical meaning of F(s)7.6.1 The IO system7.6.2 The ISO system
III NOVEL CONTROL THEORIES: TRACKING AND TRACKABILITY
8 Tracking theory
8.1 Tracking generally8.2 Tracking versus stability8.3 Perfect tracking: characterization8.3.1 On perfect tracking generally8.3.2 The IO systems8.3.3 The ISO systems8.4 Imperfect tracking: characterization8.4.1 Output space: tracking in Lyapunov sense8.4.2 Output space: tracking with FRT8.4.3 Internal dynamics space: the IO plant tracking8.4.4 The ISO plant tracking in Lyapunov sense8.4.5 State space: the ISO plant tracking with FRT8.4.6 Tracking of the ISO plant and the target set
9 Trackability theory
9.1 Trackability versus controllability9.2 Trackability definitions9.2.1 Perfect trackability9.2.2 Perfect natural trackability9.2.3 Imperfect trackability9.2.4 Imperfect natural trackability9.2.5 Imperfect elementwise trackability9.3 Perfect trackability conditions9.3.1 IO plant perfect (natural) trackability9.3.2 ISO plant perfect (natural) trackability9.4 Imperfect trackability conditions9.4.1 IO plant imperfect (natural) trackability9.4.2 ISO plant imperfect (natural) trackability
IV NOVEL TRACKING CONTROL SYNTHESIS
10 Linear tracking control (LITC)
10.1 Generating theorem10.2 LITC of the IO plants10.3 LITC of the ISO plants
11 Lyapunov Tracking Control (LTC)
11.1 Vector Lyapunov function (VLF)11.1.1 Introduction to VLF concept11.1.2 Definitions of VLF's11.1.3 VLF generalization of the classical stability theorems11.1.4 VLF forms11.2 LTC of the IO plant11.2.1 Arbitrary scalar Lyapunov function11.2.2 The irst choice of a scalar Lyapunov function11.2.3 The second choice of a scalar Lyapunov function11.2.4 Choice of a vector Lyapunov function11.3 LTC of the ISO plant11.3.1 Arbitrary scalar Lyapunov function11.3.2 Choice of a scalar Lyapunov function11.3.3 Choice of a vector Lyapunov function
12 Natural Tracking Control (NTC)
12.1 Concept of NTC12.2 NTC of the IO plant12.2.1 General consideration12.2.2 Control synthesis for specific tracking qualities12.3 NTC of the ISO plant12.3.1 General consideration12.3.2 Control synthesis for specific tracking qualities
13 NTC versus LTC
13.1 General consideration13.2 The IO plant13.3 The ISO plant
V CONCLUSION
14 On F(s)
15 On tracking and trackability
16 On tracking control
17 Recommendation
VI APPENDIXES
A Notation
A.1 AbbreviationsA.2 IndexesA.2.1 SubscriptsA.2.2 SUPERSCRIPTA.3 LettersA.3.1 Calligraphic lettersA.3.2 Fraktur lettersA.3.3 Greek lettersA.3.4 Roman lettersA.4 Names and symbolsA.4.1 NamesA.4.2 Symbols and vectorsA.5 Units
B From IO system to ISO system
C From ISO system to IO system
D Proof of Theorem 64
E Proof of Theorem 67
F Proof of Theorem 72
G Proof of Theorem 91
H Proof of Lemma 102 (Basic Lemma)
I Proof of Theorem 116
J Proof of Theorem 142
K Proof of Theorem 145
L Proof of Theorem 149
Author Index
Subject Index

Content preview from Tracking Control of Linear Systems

Chapter 6 Nondegenerate matrices

6.1 Nondegenerate and degenerate matrices

For what follows the reader will need the knowledge of definitions and properties of the greatest common (left, right) divisors of the matrix polynomials, of the unimodular matrix polynomials, as well as the knowledge of the conditions for their (left, right) coprimeness (see the books by J. P. Antsaklis and A. N. Michel [8, pp. 526-528, 535-540], C.-T. Chen [29, pp. 591-599] and T. Kailath [198, pp. 373-382]).

A rational matrix function $M (.) = M_{D}^{- 1} (.) M_{N} (.) [M (.) = M_{N} (.) M_{D}^{- 1} (.)]$ is irreducible if, and only if, its polynomial matrices M_D (.) and M_N(.) are (left and/or right) coprime (see C.-T. Chen [29, pp. 591-599] and T. Kailath [198, pp. 373-382]). The greatest ...

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Tracking Control of Linear Systems

by Lyubomir T. Gruyitch

Chapter 6 Nondegenerate matrices

6.1 Nondegenerate and degenerate matrices

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