Read Control System Synthesis: A Factorization Approach, Part I

Control System Synthesis: A Factorization Approach, Part I

Mathukumalli Vidyasagar

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Description:This book introduces the so-called stable factorization approach to the synthesis of feedback controllers for linear control systems. The key to this approach is to view the multi-input, multi-output (MIMO) plant for which one wishes to design a controller as a matrix over the fraction field F associated with a commutative ring with identity, denoted by R, which also has no divisors of zero. In this setting, the set of single-input, single-output (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R. The set of unstable, meaning not necessarily stable, control systems is then taken to be the field of fractions F associated with R in the SISO case, and the set of matrices with elements in F in the MIMO case. The central notion introduced in the book is that, in most situations of practical interest, every matrix P whose elements belong to F can be factored as a ratio of two matrices N, D whose elements belong to R, in such a way that N, D are coprime. In the familiar case where the ring R corresponds to the set of bounded-input, bounded-output (BIBO)-stable rational transfer functions, coprimeness is equivalent to two functions not having any common zeros in the closed right half-plane including infinity. However, the notion of coprimeness extends readily to discrete-time systems, distributed-parameter systems in both the continuous- as well as discrete-time domains, and to multi-dimensional systems. Thus the stable factorization approach enables one to capture all these situations within a common framework. The key result in the stable factorization approach is the parametrization of all controllers that stabilize a given plant. It is shown that the set of all stabilizing controllers can be parametrized by a single parameter R, whose elements all belong to R. Moreover, every transfer matrix in the closed-loop system is an affine function of the design parameter R. Thus problems of reliable stabilization, disturbance rejection, robust stabilization etc. can all be formulated in terms of choosing an appropriate R. This is a reprint of the book Control System Synthesis: A Factorization Approach originally published by M.I.T. Press in 198We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Control System Synthesis: A Factorization Approach, Part I. To get started finding Control System Synthesis: A Factorization Approach, Part I, you are right to find our website which has a comprehensive collection of manuals listed.
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Pages: 184

Format: PDF, EPUB & Kindle Edition

Publisher: Morgan & Claypool

Release: 2011

ISBN: 1608456625

Description: This book introduces the so-called stable factorization approach to the synthesis of feedback controllers for linear control systems. The key to this approach is to view the multi-input, multi-output (MIMO) plant for which one wishes to design a controller as a matrix over the fraction field F associated with a commutative ring with identity, denoted by R, which also has no divisors of zero. In this setting, the set of single-input, single-output (SISO) stable control systems is precisely the ring R, while the set of stable MIMO control systems is the set of matrices whose elements all belong to R. The set of unstable, meaning not necessarily stable, control systems is then taken to be the field of fractions F associated with R in the SISO case, and the set of matrices with elements in F in the MIMO case. The central notion introduced in the book is that, in most situations of practical interest, every matrix P whose elements belong to F can be factored as a ratio of two matrices N, D whose elements belong to R, in such a way that N, D are coprime. In the familiar case where the ring R corresponds to the set of bounded-input, bounded-output (BIBO)-stable rational transfer functions, coprimeness is equivalent to two functions not having any common zeros in the closed right half-plane including infinity. However, the notion of coprimeness extends readily to discrete-time systems, distributed-parameter systems in both the continuous- as well as discrete-time domains, and to multi-dimensional systems. Thus the stable factorization approach enables one to capture all these situations within a common framework. The key result in the stable factorization approach is the parametrization of all controllers that stabilize a given plant. It is shown that the set of all stabilizing controllers can be parametrized by a single parameter R, whose elements all belong to R. Moreover, every transfer matrix in the closed-loop system is an affine function of the design parameter R. Thus problems of reliable stabilization, disturbance rejection, robust stabilization etc. can all be formulated in terms of choosing an appropriate R. This is a reprint of the book Control System Synthesis: A Factorization Approach originally published by M.I.T. Press in 198We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Control System Synthesis: A Factorization Approach, Part I. To get started finding Control System Synthesis: A Factorization Approach, Part I, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Control System Synthesis: A Factorization Approach, Part I

Control System Synthesis: A Factorization Approach, Part I

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