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Symbolic Methods in Control System Analysis and Design : I E E CONTROL ENGINEERING SERIES - Neil Munro

Symbolic Methods in Control System Analysis and Design

I E E CONTROL ENGINEERING SERIES

By: Neil Munro (Editor)

Hardcover

Published: 1999
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Symbolic computing has made a significant impact in the field of control engineering. This book, which brings together contributions from leading international experts in the field, provides an up-to-date treatment of various issues in system modelling, analysis, design and synthesis methods.
The book will be of interest to postgraduate students and researchers in control engineering.

'The topic of symbolic computing has been in great need of a book to provide an up-to-date treatment of the significant impact made by it in the field of control engineering. This volume fills this need in an able and instructive manner. It is good to see the valuable expertise of the contributors reflected in its pages.' * Current Engineering Practice * 'This book is suitable for postgraduate students and researchers in control systems and would be particularly useful to those applying or intending to apply symbolic computation in the control area. The book covers wide range of topics and is a good source of information and references on this important and interesting topic.' * IEEE Control Systems *

Forewordp. xiii
Contributorsp. xvii
System Modellingp. 1
Symbolic modelling and analysis of nonlinear systemsp. 3
Introductionp. 3
Nonlinear systems and signalsp. 4
System elements and operationsp. 4
Signals and signal componentsp. 5
Nonlinear system relationshipsp. 5
Elemental equationsp. 5
Signal transformsp. 6
Multidimensional transfer functionsp. 6
Application of symbolic computationp. 7
Examplep. 8
Manual procedurep. 9
Symbolic procedurep. 11
Nonlinear system responsep. 11
Time-domain responsep. 12
Frequency-domain responsep. 13
Examplep. 14
Time-domain responsep. 14
Frequency-domain responsep. 15
Graphical user interfacep. 16
Examplep. 19
Referencesp. 21
Symbolic computation for manipulation of hierarchical bond graphsp. 23
Introductionp. 23
Modelling with bond graphsp. 24
Variablesp. 25
Bondsp. 26
Junctionsp. 26
Componentsp. 27
One-port componentsp. 27
Two-port componentsp. 27
Parametersp. 28
Constitutive relationshipsp. 28
Causalityp. 28
Hierarchical bond graphsp. 29
Representations, languages and softwarep. 31
Example: a motor generatorp. 33
Acausal bond graphp. 33
Subsystemsp. 33
System Generatorp. 36
System DCp. 37
System Loadp. 38
System Motorp. 39
System PSUp. 39
System Shaftp. 40
System structurep. 41
System ordinary differential equationsp. 42
System state matricesp. 44
System frequency responsep. 46
Numerical parameters and initial statesp. 48
System responsep. 49
Conclusionp. 50
Referencesp. 50
A survey of customised computer algebra programs for multibody dynamic modellingp. 53
Introductionp. 53
General commentsp. 53
Multibody dynamics and computer algebrap. 54
Dynamic formulations and modelling approachesp. 56
Bond graphsp. 58
Customised dynamics programs: type and applicationp. 59
Numeric methodsp. 60
Symbolic methodsp. 60
Applicationsp. 61
Multibody dynamics: historical developmentp. 62
Early dynamics programsp. 62
Pioneering symbolic dynamics programsp. 63
Second-generation symbolic programsp. 64
Continuing use of numeric programsp. 65
Programs reliant on user knowledgep. 66
Modern programsp. 66
Summaryp. 67
Concluding remarksp. 72
Referencesp. 74
System Analysisp. 79
Robust control under parametric uncertainty. Part I: analysisp. 81
Introductionp. 81
Notation and preliminariesp. 82
Parametric uncertaintyp. 84
Boundary crossing and zero exclusionp. 84
Real parameter stability marginp. 85
l[subscript 2] real parametric stability marginp. 88
l[subscript 2] stability margin for time-delay systemsp. 92
Extremal results in RPRCTp. 94
Kharitonov's theoremp. 95
The edge theoremp. 98
The generalised Kharitonov theoremp. 99
Construction of the extremal subsetp. 101
Frequency-domain results in RPRCTp. 106
Frequency-domain propertiesp. 108
Closed-loop transfer functionsp. 109
Concluding remarksp. 111
Acknowledgmentsp. 113
Referencesp. 113
Using differential and real algebra in controlp. 115
Introductionp. 115
Differential algebra: motivating examplesp. 115
The basic ideas of differential algebrap. 117
Ranking of polynomialsp. 118
Reducednessp. 118
Autoreduced setsp. 119
Remaindersp. 120
Ritt's algorithmp. 120
Application of Ritt's algorithm to identifiability problemsp. 121
Real algebra: motivating examplep. 121
Constructive methods in real algebrap. 122
Cylindrical algebraic decompositionp. 123
Quantifier eliminationp. 126
Applicationsp. 127
Stationarisable pointsp. 127
Stabilityp. 129
Curve followingp. 131
Softwarep. 133
Conclusionsp. 133
Referencesp. 133
Approximate algebraic computations of algebraic invariantsp. 135
Introductionp. 135
Models with numerical inaccuracies and classification of algebraic computation problemsp. 137
Numerical tools for approximate computationsp. 140
Issues related to numerical dependence and independence of vectorsp. 140
The SVD criterionp. 140
The Gramian criterionp. 141
Compound matricesp. 141
Selection of a best uncorrupted base for a numerically dependent setp. 142
Almost zeros of a set of polynomialsp. 146
GCD method based on ERESp. 149
The ERES method: theoretical and numerical issuesp. 150
GCD method based on matrix pencilsp. 153
Connection of P[subscript m.d] with a linear systemp. 153
Reduction of the original setp. 153
Determination of the associated pencilp. 154
LCM computation and approximate factorisation of polynomialsp. 156
Fundamental definitiosn and properties of LCM of polynomialsp. 156
Factorisation and almost factorisation of polynomialsp. 157
Algorithm for computing the LCM of many polynomialsp. 161
Applications, examples and numerical performance of methodsp. 161
Performance of the ERES and MP methodsp. 165
Performance of the LCM methodp. 166
Conclusionsp. 167
Referencesp. 167
Robust stability conditions for MIMO systems with parametric uncertaintyp. 169
Introductionp. 169
Direct Nyquist array design methodp. 170
Uncertain parametric systems and polynomial familiesp. 174
From classical to robust controlp. 176
Robust direct Nyquist array (RDNA)p. 179
Robust generalised dominance (RGD) stability theoremp. 183
Robust fundamental dominance (RFD) stability theoremp. 185
Illustrative examplesp. 187
Conclusionsp. 195
Acknowledgmentsp. 197
Referencesp. 198
Appendixesp. 199
Appendix Ap. 199
Appendix Bp. 200
Design and Synthesis Methodsp. 201
Robust control under parametric uncertainty. Part II: designp. 203
Introductionp. 203
Robust classical controller design using RPRCTp. 203
Linear programming approach to designp. 210
Fixed-order pole assignment and robust stabilisationp. 213
Robust pole assignmentp. 216
Conclusions and future directionsp. 225
Acknowledgmentsp. 226
Referencesp. 226
Dynamic sliding mode control design using symbolic algebra toolsp. 227
Introductionp. 227
Dynamic sliding mode controlp. 228
Design methodp. 231
Direct sliding mode controlp. 232
Indirect sliding mode controlp. 234
Robust design methodp. 235
Mathematica implementationp. 237
Design examplesp. 238
Conclusionp. 241
Acknowledgmentp. 242
Referencesp. 242
Appendixesp. 243
Appendix Ap. 243
Appendix Bp. 245
Appendix Cp. 247
Pole assignment for uncertain systemsp. 251
Introductionp. 251
General state-feedback pole assignment problemp. 254
Dyadic methodsp. 254
Full-rank methodsp. 258
General output-feedback pole assignment problemp. 262
Static feedbackp. 262
Dynamic feedbackp. 267
Conclusionsp. 271
Referencesp. 271
Algebraic, algebrogeometric methods and symbolic computations in linear control problemsp. 273
Introductionp. 273
Classification of computational problemsp. 275
Groebner basis computationp. 277
The solution of the cover problem via Groebner basis computationp. 279
Echelon form and canonical forms of descriptor systemsp. 284
Symbolic methods for global linearisation of pole assignment mapsp. 289
Conclusionsp. 292
Referencesp. 292
Nonlinear Systemsp. 295
Symbolic aids for modelling, analysis and synthesis of nonlinear control systemsp. 297
Introductionp. 297
Theory and toolsp. 300
Problem setupp. 300
Basic notionsp. 302
Computer algebra implementationp. 307
Modellingp. 308
Systematic modellingp. 309
System characterisationp. 312
Analysisp. 313
Synthesisp. 314
Input-output exact linearisationp. 314
State-space exact linearisationp. 315
Conclusionsp. 318
Acknowledgmentsp. 318
Referencesp. 318
Symbolic methods for global optimisationp. 321
Introductionp. 321
The spatial branch-and-bound algorithmp. 322
Outline of spatial branch-and-bound algorithmp. 322
Upper and lower bounds for spatial branch-and-bound algorithmsp. 323
Underestimators and overestimators of nonconvex functionsp. 324
A symbolic reformulation algorithmp. 325
The standard form for a nonlinear programming problemp. 325
Basic ideas of symbolic reformulation algorithmp. 326
An automatic symbolic reformulation algorithmp. 327
implementation of the spatial branch-and-bound algorithmp. 329
Numerical experimentsp. 330
Konno's bilinear programp. 330
The doughnut slice problemp. 331
Haverly's pooling problemp. 332
A six-hump camel back problemp. 333
MIMO control system diagonal dominance problemp. 334
Concluding remarksp. 336
Referencesp. 337
Solving strict polynomial inequalities by Bernstein expansionp. 339
Introductionp. 339
Notationp. 340
Problem statementp. 340
Quantifier eliminationp. 340
Bernstein expansionp. 341
Bernstein transformation of a polynomialp. 341
Sweep procedurep. 343
Selection of the sweep directionp. 343
Approximation of the solution setp. 344
Algorithmp. 345
Examplesp. 346
Conclusionsp. 350
Acknowledgmentp. 351
Referencesp. 351
Computational methods for control of dynamical systemsp. 353
Background--design and control of nonlinear systemsp. 353
Design of linear control systemsp. 355
Linearisation of nonlinear systemsp. 355
State-space and transfer-function modelsp. 356
State-space operationsp. 359
Transfer-function operationsp. 361
The linear quadratic Gaussian problemp. 362
Algebraic Riccati equationp. 363
Optimal state feedbackp. 364
Optimal stochastic state estimatorp. 365
Design of nonlinear control lawsp. 366
Controls package descriptiop. 366
Basic analysis toolsp. 367
Model representation as system objectsp. 370
Systemp. 370
MakeSystemp. 370
ShowSystem and GetResultsp. 370
Design functionsp. 371
Hirschorn and Singhp. 371
AdaptiveTrackingp. 371
ApproximateAdaptiveTrackingp. 372
Simulationp. 372
C, Matlab and Simulink code generationp. 372
Simulatep. 372
Application: adaptive control of a conical magnetic bearingp. 373
Modelp. 374
Control system designp. 375
Computing the local zero dynamicsp. 377
Design of variable structure systemsp. 378
Variable-structure control designp. 379
Slidingp. 379
Reachingp. 379
Chattering reductionp. 380
Example 7. A rotor with frictionp. 381
Computing toolsp. 382
Sliding surface computationsp. 382
Switching controlp. 383
Example 7 (continued)p. 383
Conclusionsp. 385
Referencesp. 385
Indexp. 389
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780852969434
ISBN-10: 0852969430
Series: I E E CONTROL ENGINEERING SERIES
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 412
Published: 1999
Publisher: Institution of Engineering and Technology
Country of Publication: GB
Dimensions (cm): 22.86 x 15.88  x 2.54
Weight (kg): 0.84