摘要:

The theory of the asymptotic behaviour of the root-loci of linear, time-invariant, multivariable, feedback systems is developed. It is shown that each of the system zeros attracts, and is a terminating point of, one of the root-loci, as the feedback gain tends to infinity. The root-loci, that are not attracted by the zeros, tend to infinity in a special pattern that is dictated by the eigen-properties of the elementary matrices of the system. To complete the geometric description of the asymptotic behaviour of the root-loci, the concept of infinite zeros and their order is introduced. Each infinite zero of orderrattracts one root-locus and, together withr−1 other infinite zeros of the same order, the corresponding asymptotes form a Butterworth configuration of orderraround a special point defined as a ‘ pivot ’.

ISSN:0020-7179    

DOI:10.1080/00207177608922162

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

The original Nyquist criterion is based on the comparison of the encirclement of the frequency plot of the return ratio function with the number of poles and the number of zeros of the same function to determine the closed-loop stability of a feedback system. The extensions of the return ratio idea to the stability study of multi-variable feedback systems have used the same terminology and followed a similar course. For the multi-input—output case, the use of the Nyquist criterion or its extension is by no means a simple matter. This paper establishes a new frequency stability criterion which converts the Nyquist criterion from a return ratio oriented approach to a return difference oriented one. Instead of examining the encirclement of the return ratio function to a critical point, we examine the phase change of the positive frequency of the return difference function, and the number of zeros of the positive frequency of the return difference function. This result simplifies the stability study of multi-input—output lumped systems tremendously, and covers multi-input-output distributed-parameters systems naturally. For illustration, several typical examples—single-input-output feedback systems with minimum phase or non-minimum phase open-loop transfer functions, multi-input-output feedback systems with stable or unstable open-loop transfer matrices, multi-input-output feedback systems with irrational or transcendental type distributed-parameter open-loop transfer matrices—are included.

ISSN:0020-7179    

DOI:10.1080/00207177608922163

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

Numerical investigation of an iterative procedure, called the control averaging technique, is performed in, the framework of three illustrative singular optimal control problems. Effect of various relevant parameters such as penalty constants and initial guesses on the convergence behaviour of this method is examined. For each ease considered, the control averaging iterates are found to give a close approximation to the optimal solution in relatively small computing time. Furthermore, from the viewpoint of computing time the control averaging technique is found to be about six to eight times more efficient than the gradient-like minHmethod.

ISSN:0020-7179    

DOI:10.1080/00207177608922164

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

The concept of maximally admissible sets in regulator design for linear systems is defined and investigated, and efficient computational methods for finding maximally admissible sets are presented.

ISSN:0020-7179    

DOI:10.1080/00207177608922165

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

A model reference system identification method based on the hyperstability approach is used to realize an on-line modelling system for an internal combustion engine. The performance of this method, even in the presence of non-linearity and different orders of the plant and model, is found to be satisfactory.

ISSN:0020-7179    

DOI:10.1080/00207177608922166

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

This paper presents a frequency simplification technique for simplifying a transfer function of higher dimension to a transfer function of lower dimension. It tries to match the frequency response of the two transfer functions in the best possible manner in the frequency range of interest. It compares this method with the existing methods by means of a numerical example. The advantages of this method is that it aims at minimizing the error in the phase of two transfer functions together with magnitude and simplifies the complexity of work in solving for the unknown coefficient of the assumed simplified transfer function.

ISSN:0020-7179    

DOI:10.1080/00207177608922167

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

This paper presents a study of the factorized expression of the transfer matrix corresponding to a multivariable system. Two algorithms are developed to bring a transfer matrix to a factorized canonical form; these algorithms are easily programmable in a digital computer.

ISSN:0020-7179    

DOI:10.1080/00207177608922168

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

A method is proposed for solving AX + XB = C by exploiting the concepts of controllability and tearing. The matrices manipulated are no larger than A or B, and the operation count is favourable.

ISSN:0020-7179    

DOI:10.1080/00207177608922169

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

Convex cooperative control problems of a generalized control theory and problems in optimal control theory, where a set of objectives must be satisfied, may be represented by a criterion function depending on a weighting vector μ. In the linear-quadratic case the solution is characterized by the matrix Riccati differential equation with the solution implicitly depending on a vector μ. In this paper continuity in μ of the Riccati solutions is investigated and conditions are given under which continuity holds for finite time and infinite time cases.

ISSN:0020-7179    

DOI:10.1080/00207177608922170

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor

摘要:

A new approach using the decomposition ofA(t) to study the commutative class of linear time-varying systems is presented. A simpler and computer-implemental criterion of checking the commutativity ofA(t) with its integral is given. More transparent results on solution, stability, decoupling, the controlability and observability are obtained. With the new approach, a commutative linear time-varying system can be studied in the same manner as that of a linear time-invariant system.

ISSN:0020-7179    

DOI:10.1080/00207177608922171

出版商:Taylor & Francis Group    

年代:1976

数据来源: Taylor