Multivariable Computer-controlled Systems

A Transfer Function Approach

By: Efim N. Rosenwasser, Bernhard P. Lampe

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Hardcover | 28 June 2006

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500 Pages

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Although the transfer function approach is widely used in classical control theory, computer-controlled continuous-time processes are a very important subset of periodic sampled-data systems which are not treatable using ordinary transfer functions.

The authors show how parametric transfer functions, which incorporate time-dependence, can be used to give a complete exposition of analysis and design methods for multi-input, multi-output (MIMO) sampled-data systems.

Multivariable Computer-controlled Systems is divided into three parts:

- Preliminary algebraic material necessary in later chapters.

- Control problems, important in their own right but also having a substantial bearing on what follows.

- Frequency methods for the investigation of MIMO sampled-data systems (parametric discrete-time models; stability; stochastic methods; H₂ optimization and L₂ design).

Appendices covering basic mathematical formulae and two MATLAB^(R) toolboxes round out this self-contained guide.

Industry Reviews

From the reviews:

"The monograph throws the bridge between continuous and discrete control systems. ... The authors extend known approaches to achieve a comprehensive analysis of computer control systems belonging to the class of sampled data systems. ... The book contains also an Appendix providing additional mathematical problems, description of the toolbox for optimal design multivariable sampled data systems and design towards achieving a guaranteed control system performance. The book is very interesting for researchers and graduate students who want to extend their knowledge on modern control systems." (Krzysztof Galkowski, Zentralblatt MATH, Vol. 1123 (1), 2008)

"Multivariable Computer-Controlled Systems is dedicated to the theory of multivariable control systems, and the material is presented in a formal, mathematical style. ... The book also contains several appendices, including a description of a Matlab toolbox for controller design. ... the authors have done an admirable job in collecting the necessary material in one place ... . experts will no doubt value the book for its concise presentation and its focused approach ... ." (Matthew C. Turner, IEEE Control Systems Magazine, Vol. 28, December, 2008)

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Algebraic Preliminaries
Polynomial Matrices	p. 3
Basic Concepts of Algebra	p. 3
Polynomials	p. 5
Matrices over Rings	p. 7
Polynomial Matrices	p. 10
Left and Right Equivalence of Polynomial Matrices	p. 12
Row and Column Reduced Matrices	p. 15
Equivalence of Polynomial Matrices	p. 20
Normal Rank of Polynomial Matrices	p. 21
Invariant Polynomials and Elementary Divisors	p. 23
Latent Equations and Latent Numbers	p. 26
Simple Matrices	p. 29
Pairs of Polynomial Matrices	p. 34
Polynomial Matrices of First Degree (Pencils)	p. 38
Cyclic Matrices	p. 44
Simple Realisations and Their Structural Stability	p. 49
Fractional Rational Matrices	p. 53
Rational Fractions	p. 53
Rational Matrices	p. 59
McMillan Canonical Form	p. 60
Matrix Fraction Description (MFD)	p. 63
Double-sided MFD (DMFD)	p. 73
Index of Rational Matrices	p. 74
Strictly Proper Rational Matrices	p. 77
Separation of Rational Matrices	p. 82
Inverses of Square Polynomial Matrices	p. 85
Transfer Matrices of Polynomial Pairs	p. 87
Transfer Matrices of PMDs	p. 90
Subordination of Rational Matrices	p. 94
Dominance of Rational Matrices	p. 99
Normal Rational Matrices	p. 105
Normal Rational Matrices	p. 105
Algebraic Properties of Normal Matrices	p. 110
Normal Matrices and Simple Realisations	p. 114
Structural Stable Representation of Normal Matrices	p. 116
Inverses of Characteristic Matrices of Jordan and Frobenius Matrices	p. 122
Construction of Simple Jordan Realisations	p. 126
Construction of Simple Frobenius Realisations	p. 132
Construction of S-representations from Simple Realisations. General Case	p. 136
Construction of Complete MFDs for Normal Matrices	p. 138
Normalisation of Rational Matrices	p. 141
General MIMO Control Problems
Assignment of Eigenvalues and Eigenstructures by Polynomial Methods	p. 149
Problem Statement	p. 149
Basic Controllers	p. 151
Recursive Construction of Basic Controllers	p. 154
Dual Models and Dual Bases	p. 161
Eigenvalue Assignment for Polynomial Pairs	p. 165
Eigenvalue Assignment by Transfer Matrices	p. 169
Structural Eigenvalue Assignment for Polynomial Pairs	p. 172
Eigenvalue and Eigenstructure Assignment for PMD Processes	p. 174
Fundamentals for Control of Causal Discrete-time LTI Processes	p. 183
Finite-dimensional Discrete-time LTI Processes	p. 183
Transfer Matrices and Causality of LTI Processes	p. 189
Normal LTI Processes	p. 191
Anomalous LTI Processes	p. 197
Forward and Backward Models	p. 209
Stability of Discrete-time LTI Systems	p. 222
Closed-loop LTI Systems of Finite Dimension	p. 225
Stability and Stabilisation of the Closed Loop	p. 230
Frequency Methods for MIMO SD Systems
Parametric Discrete-time Models of Continuous-time Multivariable Processes	p. 241
Response of Linear Continuous-time Processes to Exponential-periodic Signals	p. 241
Response of Open SD Systems to Exp.per. Inputs	p. 245
Functions of Matrices	p. 250
Matrix Exponential Function	p. 256
DPFR and DLT of Rational Matrices	p. 258
DPFR and DLT for Modulated Processes	p. 261
Parametric Discrete Models of Continuous Processes	p. 266
Parametric Discrete Models of Modulated Processes	p. 271
Reducibility of Parametric Discrete Models	p. 275
Description and Stability of SD Systems	p. 279
The Standard Sampled-data System	p. 279
Equation Discretisation for the Standard SD System	p. 280
Parametric Transfer Matrix (PTM)	p. 283
PTM as Function of the Argument s	p. 289
Internal Stability of the Standard SD System	p. 295
Polynomial Stabilisation of the Standard SD System	p. 298
Modal Controllability and the Set of Stabilising Controllers	p. 304
Analysis and Synthesis of SD Systems Under Stochastic Excitation	p. 307
Quasi-stationary Stochastic Processes in the Standard SD System	p. 307
Mean Variance and H₂-norm of the Standard SD System	p. 312
Representing the PTM in Terms of the System Function	p. 315
Representing the H₂-norm in Terms of the System Function	p. 325
Wiener-Hopf Method	p. 331
Algorithm for Realisation of Wiener-Hopf Method	p. 332
Modified Optimisation Algorithm	p. 336
Transformation to Forward Model	p. 340
H₂ Optimisation of a Single-loop System	p. 347
Single-loop Multivariable SD System	p. 347
General Properties	p. 348
Stabilisation	p. 353
Wiener-Hopf Method	p. 354
Factorisation of Quasi-polynomials of Type 1	p. 355
Factorisation of Quasi-polynomials of Type 2	p. 364
Characteristic Properties of Solution for Single-loop System	p. 373
Simplified Method for Elementary System	p. 374
L₂-Design of SD Systems	p. 381
Problem Statement	p. 381
Pseudo-rational Laplace Transforms	p. 383
Laplace Transforms of Standard SD System Output	p. 387
Investigation of Poles of the Image Z(s)	p. 392
Representing the Output Image in Terms of the System Function	p. 397
Representing the L₂-norm in Terms of the System Function	p. 399
Wiener-Hopf Method	p. 402
General Properties of Optimal Systems	p. 407
Modified Optimisation Algorithm	p. 409
Single-loop Control System	p. 410
Wiener-Hopf Method for Single-loop Tracking System	p. 412
L₂ Redesign of Continuous-time LTI Systems under Persistent Excitation	p. 416
L₂ Redesign of a Single-loop LTI System	p. 426
Appendices
Operator Transformations of Taylor Sequences	p. 431
Sums of Certain Series	p. 435
DirectSDM - A Toolbox for Optimal Design of Multivariable SD Systems	p. 437
Introduction	p. 437
Data Structures	p. 437
Operations with Polynomial Matrices	p. 438
Auxiliary Algorithms	p. 440
H₂-optimal Controller	p. 440
Extended Single-loop System	p. 440
Function sdh2	p. 442
L₂-optimal Controller	p. 443
Extended Single-loop System	p. 443
Function sdl2	p. 445
Design of SD Systems with Guaranteed Performance	p. 447
Introduction	p. 447
Design for Guaranteed Performance	p. 448
System Description	p. 448
Problem Statement	p. 450
Calculation of Performance Criterion	p. 451
Minimisation of Performance Criterion Estimate for SD Systems	p. 452
MATLAB“-Toolbox GarSD	p. 453
Structure	p. 453
Setting Properties of External Excitations	p. 454
Investigation of SD Systems	p. 455
References	p. 461
Index	p. 473
Table of Contents provided by Publisher. All Rights Reserved.

Multivariable Computer-controlled Systems

A Transfer Function Approach

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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