Trackability and tracking of general linear systems
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Cover Half Title Title Copyright Contents Preface Part I SYSTEM CLASSES Chapter 1 Introduction 1.1 Time 1.2 Time, physical principles, and systems 1.3 Notational preliminaries 1.4 Compact, simple, and elegant calculus 1.5 Time and system behavior 1.6 Time and control 1.7 System transfer function matrices 1.8 Full block diagrams: control systems 1.8.1 Full block diagrams 1.8.2 FCS(s) of the open loop control system 1.8.3 FCS(s) of the closed loop control system 1.8.4 FCS(s) of the combined loops control system 1.9 Matrix functions and polynomials Chapter 2 IO systems 2.1 IO system mathematical model 2.1.1 Time domain 2.1.2 Complex domain 2.2 IO plant desired regime 2.3 IO feedback controller 2.3.1 Time domain 2.3.2 Complex domain 2.4 Exercises Chapter 3 ISO systems 3.1 ISO system mathematical model 3.1.1 Time domain 3.1.2 Complex domain 3.2 ISO plant desired regime 3.3 ISO feedback controller 3.3.1 Time domain 3.3.2 Complex domain 3.4 Exercises Chapter 4 EISO systems 4.1 EISO system mathematical model 4.1.1 Time domain 4.1.2 Complex domain 4.2 EISO plant desired regime 4.3 EISO feedback controller 4.3.1 Time domain 4.3.2 Complex domain 4.4 Exercises Chapter 5 HISO systems 5.1 HISO system mathematical model 5.1.1 Time domain 5.1.2 Complex domain 5.2 The HISO plant desired regime 5.3 HISO feedback controller 5.3.1 Time domain 5.3.2 Complex domain 5.4 Exercises Chapter 6 IIO systems 6.1 IIO system mathematical model 6.1.1 Time domain 6.1.2 Complex domain 6.2 IIO plant desired regime 6.3 IIO feedback controller 6.3.1 Time domain 6.3.2 Complex domain 6.4 Exercises Part II TRACKING Chapter 7 Fundamental control principle 7.1 Control axiom 7.2 Control perpetuum mobile Chapter 8 Tracking fundamentals 8.1 Control goal and tracking concepts 8.1.1 Control purpose and tracking 8.1.2 Basic tracking meaning 8.2 Perfect tracking 8.3 Imperfect infinite-time tracking 8.3.1 Introduction 8.3.2 Tracking in the Lyapunov sense 8.3.3 Tracking versus stability 8.3.4 Stablewise tracking in general 8.3.5 Exponential tracking 8.4 Tracking with finite reachability time 8.5 Finite scalar reachability time 8.6 Finite vector reachability time Part III TRACKABILITY Chapter 9 Trackability fundamentals 9.1 Trackability of a plant and its regime 9.2 Trackability versus controllability 9.3 Tracking demands trackability 9.4 Perfect trackability: various types 9.4.1 Perfect and elementwise perfect trackability 9.4.2 Trackability and nature 9.4.3 Perfect and elementwise perfect natural trackability . . 9.5 Imperfect trackability: various types 9.5.1 Imperfect trackability 9.5.2 Imperfect natural trackability 9.5.3 Elementwise trackability 9.5.4 Elementwise natural trackability Chapter 10 Various systems trackability 10.1 IO system trackability 10.1.1 Perfect trackability criteria 10.1.2 Conditions for perfect natural trackability 10.1.3 Imperfect trackability criteria 10.1.4 Conditions for natural trackability 10.2 ISO system trackability 10.2.1 Perfect trackability criteria 10.2.2 Conditions for perfect natural trackability 10.2.3 Imperfect trackability criteria 10.2.4 Conditions for imperfect natural trackability 10.3 EISO system trackability 10.3.1 Perfect trackability criteria 10.3.2 Conditions for perfect trackability 10.3.3 Conditions for perfect natural trackability 10.3.4 Imperfect trackability criteria 10.3.5 Conditions for natural trackability 10.4 HISO system trackability 10.4.1 Perfect trackability criteria 10.4.2 Conditions for perfect natural trackability 10.4.3 Imperfect trackability criteria 10.4.4 Conditions for imperfect natural trackability 10.5 IIO system trackability 10.5.1 Perfect trackability criteria 10.5.2 Conditions for perfect natural trackability 10.5.3 Imperfect trackability criteria 10.5.4 Conditions for imperfect natural trackability Part IV TRACKING CONTROL Chapter 11 Linear tracking control (LiTC) 11.1 Common systems descriptions 11.1.1 Plants descriptions 11.1.2 Controllers descriptions 11.1.3 Control systems descriptions 11.1.4 Generating theorem 11.1.5 Tracking conditions and control Chapter 12 Lyapunov Tracking Control (LyTC) 12.1 General form of the linear systems 12.1.1 Introduction 12.1.2 EISO form of the IO systems 12.1.3 EISO form of the ISO systems 12.1.4 EISO form of the EISO systems 12.1.5 EISO form of the HISO systems 12.1.6 EISO form of the IIO systems 12.2 Lyapunov tracking theory basis 12.2.1 Lyapunov matrix theorem 12.2.2 Arbitrary scalar Lyapunov function 12.2.3 Quadratic form as a Lyapunov function 12.2.4 Introduction to VLF concept 12.2.5 Definitions of VLFs 12.2.6 VLF generalization of the classical stability theorems . 12.2.7 VLF forms 12.2.8 Choice of a vector Lyapunov function Chapter 13 Natural Tracking Control (NTC) 13.1 High quality tracking criteria 13.1.1 Time vectors and time sets 13.1.2 Subsidiary reference output 13.1.3 Tracking quality criterion 13.2 NTC concept and definition 13.3 NTC origin and development 13.4 NTC of linear systems 13.4.1 General consideration 13.4.2 Control synthesis for specific tracking qualities Part V APPENDIX A Notation A.1 Abbreviations A.2 Indexes A.2.1 SUBSCRIPTS A.2.2 SUPERSCRIPT A.3 Letters A.3.1 CALLIGRAPHIC LETTERS A.3.2 FRAKTUR LETTERS A.3.3 GREEK LETTERS A.3.4 ROMAN LETTERS A.4 Name A.5 Symbols, vectors, sets, and matrices A.6 Units B Equivalent definitions B.1 Equivalent tracking definitions B.1.1 Equivalent imperfect tracking definitions B.1.2 Equivalent exponential tracking definition B.2 Equivalent trackability definitions B.2.1 Equivalent definitions of perfect trackability B.2.2 Equivalent definition of imperfect trackability B.2.3 Equivalent definition of natural trackability B.2.4 Equivalent definition of elementwise trackability B.2.5 Elementwise natural trackability C Example C.1 Example of f (:)-function D Proofs D.1 Proof of Theorem 67 D.2 Proof of Theorem 72 D.3 Proof of Theorem 126 E Transformations E.1 Transformation of IO into ISO system E.2 ISO and EISO forms of IIO system Part VI INDEX Author Index Subject Index
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