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E-raamat: Trackability and Tracking of General Linear Systems

(University of Technology of BelfortMontbéliard, France (Retired))
  • Formaat: 396 pages
  • Ilmumisaeg: 31-Oct-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9780429778100
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  • Formaat: 396 pages
  • Ilmumisaeg: 31-Oct-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9780429778100
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Trackability and Tracking of General Linear Systems deals with five classes of the systems, three of which are new, begins with the definition of time together with a brief description of its crucial properties and with the principles of the physical uniqueness and continuity of physical variables. They are essential for the natural tracking control synthesis. The book presents further new results on the new compact, simple and elegant calculus that enabled the generalization of the transfer function matrix concept and of the state concept, the completion of the trackability and tracking concepts together with the proofs of the trackability and tracking criteria, as well as the natural tracking control synthesis for all five classes of the systems.

Features

Crucially broadens the state space concept and the complex domain fundamentals of the dynamical systems to the control systems.

Addresses the knowledge and ability necessary to study and design control systems that will satisfy the fundamental control goal.

Outlines new effective mathematical means for effective complete analysis and synthesis of the control systems.

Upgrades, completes and essentially generalizes the control theory beyond the existing boundaries.

Provides information necessary to create and teach advanced inherently upgraded control courses.
Preface xi
I System Classes 1(108)
1 Introduction
3(34)
1.1 Time
3(3)
1.2 Time, physical principles, and systems
6(2)
1.3 Notational preliminaries
8(4)
1.4 Compact, simple, and elegant calculus
12(1)
1.5 Time and system behavior
13(9)
1.6 Time and control
22(4)
1.7 System transfer function matrices
26(2)
1.8 Full block diagrams: control systems
28(7)
1.8.1 Full block diagrams
28(2)
1.8.2 Fcs(s) of the open loop control system
30(2)
1.8.3 Fcs(s) of the closed loop control system
32(2)
1.8.4 Fcs(s) of the combined loops control system
34(1)
1.9 Matrix functions and polynomials
35(2)
2 IO systems
37(16)
2.1 IO system mathematical model
37(9)
2.1.1 Time domain
37(3)
2.1.2 Complex domain
40(6)
2.2 IO plant desired regime
46(3)
2.3 IO feedback controller
49(2)
2.3.1 Time domain
49(1)
2.3.2 Complex domain
49(2)
2.4 Exercises
51(2)
3 ISO systems
53(12)
3.1 ISO system mathematical model
53(5)
3.1.1 Time domain
53(2)
3.1.2 Complex domain
55(3)
3.2 ISO plant desired regime
58(2)
3.3 ISO feedback controller
60(2)
3.3.1 Time domain
60(1)
3.3.2 Complex domain
60(2)
3.4 Exercises
62(3)
4 EISO systems
65(18)
4.1 EISO system mathematical model
65(12)
4.1.1 Time domain
65(4)
4.1.2 Complex domain
69(8)
4.2 EISO plant desired regime
77(1)
4.3 EISO feedback controller
78(4)
4.3.1 Time domain
78(1)
4.3.2 Complex domain
79(3)
4.4 Exercises
82(1)
5 HISO systems
83(12)
5.1 HISO system mathematical model
83(6)
5.1.1 Time domain
83(1)
5.1.2 Complex domain
84(5)
5.2 The HISO plant desired regime
89(2)
5.3 HISO feedback controller
91(3)
5.3.1 Time domain
91(1)
5.3.2 Complex domain
91(3)
5.4 Exercises
94(1)
6 IIO systems
95(14)
6.1 IIO system mathematical model
95(7)
6.1.1 Time domain
95(2)
6.1.2 Complex domain
97(5)
6.2 IIO plant desired regime
102(2)
6.3 IIO feedback controller
104(4)
6.3.1 Time domain
104(1)
6.3.2 Complex domain
105(3)
6.4 Exercises
108(1)
II Tracking 109(40)
7 Fundamental control principle
111(2)
7.1 Control axiom
111(1)
7.2 Control perpetuum mobile
112(1)
8 Tracking fundamentals
113(36)
8.1 Control goal and tracking concepts
113(4)
8.1.1 Control purpose and tracking
113(1)
8.1.2 Basic tracking meaning
114(3)
8.2 Perfect tracking
117(2)
8.3 Imperfect infinite-time tracking
119(12)
8.3.1 Introduction
119(1)
8.3.2 Tracking in the Lyapunov sense
119(2)
8.3.3 Tracking versus stability
121(1)
8.3.4 Stablewise tracking in general
122(7)
8.3.5 Exponential tracking
129(2)
8.4 Tracking with finite reachability time
131(1)
8.5 Finite scalar reachability time
131(6)
8.6 Finite vector reachability time
137(12)
III Trackability 149(74)
9 Trackability fundamentals
151(16)
9.1 Trackability of a plant and its regime
151(1)
9.2 Trackability versus controllability
152(1)
9.3 Tracking demands trackability
153(1)
9.4 Perfect trackability: various types
153(6)
9.4.1 Perfect and elementwise perfect trackability
153(3)
9.4.2 Trackability and nature
156(1)
9.4.3 Perfect and elementwise perfect natural trackability
157(2)
9.5 Imperfect trackability: various types
159(8)
9.5.1 Imperfect trackability
159(2)
9.5.2 Imperfect natural trackability
161(2)
9.5.3 Elementwise trackability
163(1)
9.5.4 Elementwise natural trackability
164(3)
10 Various systems trackability
167(56)
10.1 IO system trackability
167(14)
10.1.1 Perfect trackability criteria
167(6)
10.1.2 Conditions for perfect natural trackability
173(2)
10.1.3 Imperfect trackability criteria
175(3)
10.1.4 Conditions for natural trackability
178(3)
10.2 ISO system trackability
181(11)
10.2.1 Perfect trackability criteria
181(4)
10.2.2 Conditions for perfect natural trackability
185(1)
10.2.3 Imperfect trackability criteria
186(3)
10.2.4 Conditions for imperfect natural trackability
189(3)
10.3 EISO system trackability
192(10)
10.3.1 Perfect trackability criteria
192(1)
10.3.2 Conditions for perfect trackability
193(2)
10.3.3 Conditions for perfect natural trackability
195(2)
10.3.4 Imperfect trackability criteria
197(3)
10.3.5 Conditions for natural trackability
200(2)
10.4 HISO system trackability
202(10)
10.4.1 Perfect trackability criteria
202(3)
10.4.2 Conditions for perfect natural trackability
205(2)
10.4.3 Imperfect trackability criteria
207(2)
10.4.4 Conditions for imperfect natural trackability
209(3)
10.5 IIO system trackability
212(13)
10.5.1 Perfect trackability criteria
212(3)
10.5.2 Conditions for perfect natural trackability
215(1)
10.5.3 Imperfect trackability criteria
216(3)
10.5.4 Conditions for imperfect natural trackability
219(4)
IV Tracking Control 223(62)
11 Linear tracking control (LiTC)
225(12)
11.1 Common systems descriptions
225(12)
11.1.1 Plants descriptions
225(1)
11.1.2 Controllers descriptions
226(1)
11.1.3 Control systems descriptions
227(5)
11.1.4 Generating theorem
232(1)
11.1.5 Tracking conditions and control
233(4)
12 Lyapunov Tracking Control (LyTC)
237(20)
12.1 General form of the linear systems
237(5)
12.1.1 Introduction
237(1)
12.1.2 EISO form of the IO systems
238(1)
12.1.3 EISO form of the ISO systems
238(1)
12.1.4 EISO form of the EISO systems
238(1)
12.1.5 EISO form of the HISO systems
238(2)
12.1.6 EISO form of the IIO systems
240(2)
12.2 Lyapunov tracking theory basis
242(15)
12.2.1 Lyapunov matrix theorem
242(2)
12.2.2 Arbitrary scalar Lyapunov function
244(3)
12.2.3 Quadratic form as a Lyapunov function
247(2)
12.2.4 Introduction to VLF concept
249(1)
12.2.5 Definitions of VLFs
250(2)
12.2.6 VLF generalization of the classical stability theorems
252(1)
12.2.7 VLF forms
253(1)
12.2.8 Choice of a vector Lyapunov function
254(3)
13 Natural Tracking Control (NTC)
257(28)
13.1 High quality tracking criteria
257(13)
13.1.1 Time vectors and time sets
257(1)
13.1.2 Subsidiary reference output
257(4)
13.1.3 Tracking quality criterion
261(9)
13.2 NTC concept and definition
270(2)
13.3 NTC origin and development
272(1)
13.4 NTC of linear systems
273(14)
13.4.1 General consideration
273(7)
13.4.2 Control synthesis for specific tracking qualities
280(5)
V Appendix 285(80)
A Notation
287(18)
A.1 Abbreviations
287(1)
A.2 Indexes
288(1)
A.2.1 Subscripts
288(1)
A.2.2 Superscript
288(1)
A.3 Letters
289(12)
A.3.1 Calligraphic Letters
289(1)
A.3.2 Fraktur Letters
290(3)
A.3.3 Greek Letters
293(1)
A.3.4 Roman Letters
294(7)
A.4 Name
301(1)
A.5 Symbols, vectors, sets, and matrices
301(3)
A.6 Units
304(1)
B Equivalent definitions
305(10)
B.1 Equivalent tracking definitions
305(4)
B.1.1 Equivalent imperfect tracking definitions
305(3)
B.1.2 Equivalent exponential tracking definition
308(1)
B.2 Equivalent trackability definitions
309(6)
B.2.1 Equivalent definitions of perfect trackability
309(1)
B.2.2 Equivalent definition of imperfect trackability
310(1)
B.2.3 Equivalent definition of natural trackability
311(1)
B.2.4 Equivalent definition of elementwise trackability
312(1)
B.2.5 Elementwise natural trackability
313(2)
C Example
315(2)
C.1 Example of f(.)-function
315(2)
D Proofs
317(10)
D.1 Proof of Theorem 67
317(3)
D.2 Proof of Theorem 72
320(4)
D.3 Proof of Theorem 126
324(3)
E Transformations
327(38)
E.1 Transformation of IO into ISO system
327(2)
E.2 ISO and EISO forms of IIO system
329(36)
VI Index 365(2)
Author Index 367(2)
Subject Index 369
Mr. Lyubomir T. Gruyitch is Certified Mechanical Engineer (Dipl. M. Eng.), Master of Electrical Engineering Sciences (M. E. E. Sc.), and Doctor of Engineering Sciences (D. Sc.) (All with the University of Belgrade, Serbia). Dr. Gruyitch was a leading contributor to the creation of the research Laboratory of Automatic Control, Mechatronics, Manufacturing Engineering and Systems Engineering of the National School of Engineers (Belfort, France), and a founder of the educational and research Laboratory of Automatic Control of the FME. He has published 13 books (in: English 12, Serb 1), 4 textbooks (in: Serb), 11 lecture notes (in: English 2, French 7, Serb 2), one manual of solved problems (in: Serb), one book translation from Russian, chapters in eight scientific books, 130 scientific papers in scientific journals, 173 conference research papers and two educational papers. Professor Gruyitch supervised one doctorate at the University of Technology Belfort-Montbeliard - UTBM (France), which gained the highest grade by an international (French - USA) jury, five doctorates at the University of Belgrade (Serbia), four DEA (equivalent to M. Sc.) theses at the ENI and five master theses at the University of Belgrade. Professor Gruyitch was a co-initiator of the proposal for a new tentative, highly advanced, Department of Automatique et Systémique at the UTBM, and the Coordinator of the team that worked out the full project. He was cofounder of the Cathedra of Automatic Control and of the undergraduate and graduate Group of Automatic Control of the FME. He introduced a number of new courses at the universities in France, South Africa and Serbia. He was the principal investigator supervising several projects funded by industry in Serbia. Professor Gruyitch was a member of the Acting Senate of the UTBM and the Coordinator of the Commission of Research of the UTBM. He was the Chief of the Cathedra of Automatic Control, the Chief of the Laboratory of Automatic Control and the President of the Senate of the Faculty of Mechanical Engineering, Belgrade. Dr. Gruyitch gave invited university seminars in Belgium, Canada, England, France, Russia, Serbia, Tunis and USA. He was invited plenary sessions speaker, Organizer and/or Chairman of invited sessions at the international conferences, and President of the International Program Committee of the IFAC - IFIP - IMACS Conference Control of Industrial Systems, Belfort, France (more than 300 participants from 42 countries with four continents).