Linear control systems: 2 Synthesis of multivariable systems and multidimensional systems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Taunton
Research Studies Press u.a.
1993
|
| Series: | Industrial control, computers and communications series
7 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 378 S. |
| ISBN: | 0863801277 0471934348 |
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MARC
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| adam_text | ix
Contents
Preface to Volume 2
CHAPTER 1. LINEAR SYSTEMS WITH FEEDBACK 1
1.1 Systems with Static and Dynamic Feedbacks 1
1.1.1 Formulation of the pole assignment problem 1
1.1.2 Formulation of the factor assignment problem 5
1.1.3 Dependence of pole positions of the feedbacks 6
1.1.4 Invariance of the zeros of the closed loop system
under feedbacks 8
1.1.5 Determination of the state feedback for a closed loop
system controllable by a single input 12
1.2 Solution of the Pole Assignment Problem 15
1.2.1 Solution of the pole assignment problem with static
state feedback for single input systems 15
1.2.2 Solution of the pole assignment problem with static
state feedback for multi input systems 18
1.2.3 Determination of the state feedback for a closed loop
system controllable by a single input with a cyclic
system matrix 23
1.2.4 Closed loop eigenstructure assignment with state
feedback 25
1.2.5 Pole assignment with unity rank state feedback 31
1.2.6 Pole assignment with output feedback 33
1.2.7 Unattainability of certain pole positions in single
input systems with output feedback 40
1.2.8 Transfer matrix approach to the pole assignment
problem with state feedback 43
1.3 Invariant Factor Assignment 47
X
1.3.1 Invariant factor assignment with state feedback 47
1.3.2 Factor assignment with dynamic output feedback 54
1.3.3 Factor assignment with state feedback in
generalised systems 64
1.3.4 Transfer matrix approach to the pole assignment
problem with state feedback in generalised systems 71
1.3.5 Invariant factor assignment with periodic feedback 77
1.3.5.1 Invariant factor assignment with state
feedback 77
1.3.5.2 Invariant factor assignment with periodic
output feedback 84
1.4 Observers 88
1.4.1 Full order asymptotic observers of regular linear
systems 88
1.4.2 Regular system with an observer and a state
feedback 91
1.4.3 Reduced order asymptotic observers of regular
linear systems 92
1.4.4 Reduced order asymptotic observers of generalised
systems 100
1.4.5 Deadbeat observers for generalised systems 107
1.5 Problems 108
References 110
CHAPTER 2. (A^) INVARIANT SUBSPACES,
CONTROLLABILITY SUBSPACES AND
GENERALISED OUTPUT NULLING SUBSPACES 115
2.1 (A.B) Invariant Subspaces 115
2.1.1 Basic notions 115
2.1.2 Computation of sup J (A,B,W) 118
2.1.3 Observability of linear systems with unknown
inputs 121
2.1.4 Computation of sup J (A.B.ker C) 125
2.1.5 Disturbance decoupling 127
2.2 Controllability Subspaces 131
2.3 Supremal Controllability Subspaces 136
2.3.1 Computation of sup C (A.B.ker D) 139
2.4 Generalised Output Nulling Subspaces 141
2.4.1 Definition and computation of generalised output
nulling subspaces 141
2.4.2 Some subspaces related to observability,
constructibility, reachability and controllability 147 j
xi
2.5 Output Nulling and Unknown Input Subspaces for
Singular Systems 161
2.5.1 Output nulling problem and basic definitions 151
2.5.2 Computation of Vk, Ck, Rk, and Uk 153
2.6 Problems 157
References 159
CHAPTER3. SYNTHESIS OF LINEAR SYSTEMS 162
3.1 Internal Stabilisation of Linear Systems 162
3.1.1 Basic notions 162
3.1.2 Internal stabilisation of linear systems 163
3.2 General Feedback Control Problem 170
3.2.1 Formulation of general feedback control problem 170
3.2.2 Kucera Youla parameterisation and the internal
stabilisation problem 172
3.2.3 Solvability conditions 174
3.2.4 Tracking and regulation in the presence of
disturbances 184
3.3 Some Particular Cases of Problem 3.1 188
3.3.1 Disturbance decoupling problem 188
3.3.2 Exact model matching problem 188
3.3.3 Unity feedback compensation problem 189
3.3.4 Observer problem 190
3.4 Polynomial Equation Approach 192
3.4.1 Deadbeat servo problem 192
3.4.1.1 Single input single output systems 192
3.4.1.2 Multivariable systems 195
3.4.2 Exact model matching problem 202
3.4.2.1 Problem formulation 202
3.4.2.2 Problem solution 203
3.4.3 Optimal regulator problem 208
3.4.4 Optimal tracking problem 215
3.5 Problems 221
References 223
SYSTEMS 228
4.1 Models of Generalised Multidimensional Systems 228
4.1.1 Relationships between models 231
4.1.2 Reduction of multidimensional models to equivalent
1 D models 234
xii
4.2 Existence and Uniqueness of Solutions to Multidimensional
Models 237
4.2.1 Existence of solution to the G2 DM in a given
rectangle 237
4.2.2 Solvability conditions and uniqueness in the 2 D
Z domain 243
4.2.3 Boundary values and conditionability of the G2 DM 251
4.2.4 Existence and determination of admissible boundary
conditions 252
4.2.5 Existence and uniqueness of the solution to the
generalised 2 D model with special boundary
conditions 260
4.3 Response Formula and Shuffle Algorithm for Generalised
2 D Model 273
4.3.1 Response formula 273
4.3.2 Extension of the Cayley Hamilton theorem for the
G2 DM 280
4.3.3 Testing of the regularity of the G2 DM 280
4.3.4 The 2 D shuffle algorithm 283
4.4 Local Reachability, Local Controllability and Optimal
Control of the G2 DM 289
4.4.1 Local reachability and local controllability 289
4.4.2 Minimum energy control 292
4.4.3 Linear quadratic optimal regulator for the G2 DM
with variable coefficients 294
4.4.4 Global observability and reconstructibility 298
4.4.5 Causal observability and reconstructibility 301
4.5 Asymptotic and Deadbeat 2 D Observers 305
4.6 Equivalence and Similarity 308
4.6.1 Input output equivalence and strict equivalence of
system matrices 308
4.6.2 Similarity of system matrices 311
4.7 (E,A,B) Invariant Subspaces and Disturbance Decoupling
Problem 312
4.7.1 (E,A,B) invariant subspaces 312
4.7.2 Disturbance decoupling problem 314
4.8 Invertibility of Generalised 2 D Linear Systems 315
4.8.1 Approach based on the left inverse of the transfer
matrix 315
4.8.2 Approach based on transition matrices 318
4.8.3 Approach based on system matrices 322
4.8.4 Poles, zeros and the asymptotically stable inverse 322 j
xiii
4.9 Problems 324
References 327
APPENDIX A. POLYNOMIAL MATRIX EQUATIONS 330
A.I Unilateral Polynomial Matrix Equations 330
A.2 Minimum Degree Solutions 337
A.3 Solak s Method 340
A.4 Bilateral Polynomial Matrix Equations 345
A.5 Skew Prime Polynomial Matrices 350
A.6 Wolovich s Method 354
A.7 Some Transformations of Bilateral Polynomial Matrix
Equations 359
A.8 Zak s Method 361
A.9 Rational Solutions to Polynomial Matrix Equations 366
A. 10 Two Polynomial Matrix Equations 368
A. 11 Problems 375
References 376
Index 377
|
| any_adam_object | 1 |
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| id | DE-604.BV008622587 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:22:01Z |
| institution | BVB |
| isbn | 0863801277 0471934348 |
| language | Undetermined |
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| physical | XIII, 378 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Research Studies Press u.a. |
| record_format | marc |
| series | Industrial control, computers and communications series |
| series2 | Industrial control, computers and communications series |
| spelling | Kaczorek, Tadeusz 1932- Verfasser (DE-588)110868889 aut Linear control systems 2 Synthesis of multivariable systems and multidimensional systems T. Kaczorek Taunton Research Studies Press u.a. 1993 XIII, 378 S. txt rdacontent n rdamedia nc rdacarrier Industrial control, computers and communications series 7 Industrial control, computers and communications series ... (DE-604)BV008622571 2 Industrial control, computers and communications series 7 (DE-604)BV000645478 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005670019&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaczorek, Tadeusz 1932- Linear control systems Industrial control, computers and communications series |
| title | Linear control systems |
| title_auth | Linear control systems |
| title_exact_search | Linear control systems |
| title_full | Linear control systems 2 Synthesis of multivariable systems and multidimensional systems T. Kaczorek |
| title_fullStr | Linear control systems 2 Synthesis of multivariable systems and multidimensional systems T. Kaczorek |
| title_full_unstemmed | Linear control systems 2 Synthesis of multivariable systems and multidimensional systems T. Kaczorek |
| title_short | Linear control systems |
| title_sort | linear control systems synthesis of multivariable systems and multidimensional systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005670019&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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