Control System Synthesis : A Factorization Approach
Control System Synthesis : A Factorization Approach
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发表时间：
1988
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通讯作者：
M. Vidyasagar
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作者：
M. Vidyasagar
这本书介绍了所谓的“稳定因子分解方法”，以综合反馈控制器的线性控制系统。这种方法的关键是查看多输入，多输出（MIMO）工厂，其中希望将控制器设计为分数域F上的矩阵，该矩阵与具有单位的交换环相关联，表示为R，其也没有零因子。在这种情况下，单输入单输出（SISO）稳定控制系统的集合恰好是环R，而稳定MIMO控制系统的集合是元素都属于R的矩阵的集合。不稳定的集合，意思是不一定稳定，控制系统在SISO情况下被认为是与R相关的分数F的域，在MIMO情况下被认为是元素在F中的矩阵的集合。书中介绍的中心概念是，在大多数实际情况下，每个矩阵P的元素都属于F，它可以被分解成两个矩阵N，D的元素都属于R的“比值”，使得N，D是互素数。在熟悉的情况下，环R对应于有界输入、有界输出（BIBO）稳定有理传递函数的集合，协素性等价于两个函数在包括无穷远的封闭右半平面上没有公共零。然而，同素性的概念很容易扩展到离散时间系统，连续和离散时间域中的分布参数系统，以及多维系统。因此，稳定分解方法使人们能够在一个公共框架内捕获所有这些情况。稳定分解方法的关键结果是稳定给定对象的所有控制器的参数化。结果表明，所有稳定控制器的集合可以用一个参数R来参数化，R的元素都属于R，并且闭环系统中的每个传递矩阵都是设计参数R的仿射函数。因此，可靠镇定、抗扰、鲁棒镇定等问题都可以用选择合适的R来表示。《因数分解方法》最初由麻省理工学院出版社于1985年出版。目录：导论/固有稳定有理函数/标量系统：导论/矩阵环/稳定化
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 1985. Table of Contents: Introduction / Proper Stable Rational Functions / Scalar Systems: An Introduction / Matrix Rings / Stabilization