摘要:

The properties of a linear matrix feedback system with two degrees of freedom which allows Rosenbrock's direct Nyquist array design method to be extended to the case of uncertain multivariable systems are examined. Criteria for assessing the global and loop disturbance rejection properties of a multivariable control system are developed, and a design methodology for uncertain multivariable plants, subject to external disturbance inputs is given. The proposed design method is illustrated by means of an example.

ISSN:0020-7179    

DOI:10.1080/00207178408933317

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Linear control systems of the form E dx/dt = Ax;+ Bu, y = Cx + Du are considered, where E and A are not necessarily square matrices, and no assumption is made on the rank of the matrix pencil sE⁢— A. The problem to be solved is this : find a system of the form Édz/dt = Âz + [Bcirc]ŷ, u = Ĉz + [Dcirc]ŷ where ŷ is some linear combination of y (the output of the original system) and its derivatives, and u is the input of the original system. For the solution of this problem, a method (based on the use of matrix generalized inverses) is developed that can be applied both to time-invariant and time-varying systems, A numerical procedure is elaborated for the time-invariant case that either yields a system Ê dz/dt = Âz + [Bcirc]ŷ, u =Ĉz ⁢+ [Dcirc]ý (in which the coefficient matrices are of the smallest possible dimensions), or it shows that there is no such system. This procedure makes use of a recent paper of Wilkinson on singular systems of linear differential equations. In the special case where E =I, the procedure of this paper yields a minimal left inverse of the original system if a left inverse exists.

ISSN:0020-7179    

DOI:10.1080/00207178408933318

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A method is presented for constructing a model of a non-linear system from the input-output data. The structure of the system is assembled from a library of nonlinear terms that are possible suspects for inclusion in the model. While each possible model structure is represented by a node in a tree, it is shown that searching the tree for the optimal n-term model structure can be done in n stages using an algorithm based on conjugate direction ideas. The essential feature of the technique is that it generates a sequence of projection matrices such that the original vector-valued functions become conjugate directions. This leaves the original non-linear terms intact and allows the structure for the optimal n-term model to be assembled in n selections from the library. Examples are presented from regression analysis and non-linear dynamic systems.

ISSN:0020-7179    

DOI:10.1080/00207178408933319

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

This paper presents a unified treatment of aggregability, lumpability, coherency, reversibility, partial balance and similar properties appearing in different fields including power systems and queueing theory. A coherency condition, well known in power systems, implies the existence of a finite state filter for Markov chains, while aggregability and coherency yield a new condition for decentralized computation of the invariant measure.

ISSN:0020-7179    

DOI:10.1080/00207178408933320

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The problem of stabilizing a nonlinear system by the application of additive output feedback is considered. It is shown that if an infective recursive system σ can be so stabilized, then it must be rational, namely, it must be possible to express σ as a ratio Y. = PQ-lof two stable and recursive systems P and Q.

ISSN:0020-7179    

DOI:10.1080/00207178408933321

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The choice of a parametrization for the representation of a linear multivariable control system amounts to the selection of a basis of the rows of the Hankel matrix of Markov elements. The so-called ‘ overlapping ’ or ‘ pseudo-canonical ’ forms are traditionally obtained by imposing two selection rules : a block selection rule and a chain selection rule. In this paper, these constraints are relaxed to requiring only a chain selection rule. This allows for more flexibility in selecting numerically well-conditioned parametrizations.

ISSN:0020-7179    

DOI:10.1080/00207178408933322

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

There is given a constrained plant P described by a partial differential equation (PDE) in two variables t and x. Owing to uncertainty P belongs to a given set 𝒮There are assigned tolerances on the system response to command and/or disturbances, to be achieved over the defined t and x intervals for all P in 𝒮. Previous treatment was confined to systems causal in both t and x. This work extends quantitative synthesis to systems causal in l and non-causal in x. Frequency response methods in two complex variables are presented, which are generalizations of quantitative synthesis techniques for lumped systems. The principal treatment is to (a) t in [0, ∞), x in ( — ∞, ∞) and (b) t in [0, ∞), x in [0, ], Consideration is also given to uncertain non.linear PDE plants.

ISSN:0020-7179    

DOI:10.1080/00207178408933323

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

This paper is devoted to the stable linear time-invariant plant whose transfer function P{s) has right half-plane (RHP) zeros, denoted as a non-minimum-phase (NMP) plant. We can always write P(s) = Pm(s)A(s), | A(jw)| = 1, arg A(jm) raonotonically decreasing from zero at W = 0, and Pmminimum-phase (MP). In the traditional design, the plant loop transmission L(s) has |L(jw) | > 1 for w in [0, wc), < 1 for w;> wc, the cross-over frequency. The benefits of feedback are then restricted to [0, wc) with wc, < wc. If P(s) is MP, wcmay theoretically be arbitrarily large but in the NMP ease wc< Wa, given approximately by arg A(JW )= — 60°. It is shown that other options are available in NMP systems, by having several cross-over frequencies. If A (s) has finite degree, it is even theoretically possible to achieve arbitrarily large | L(jw) | over an arbitrarily large-frequency range (w1, w2). However, the price is paid with one or more ‘holes’ (finite-frequency ranges) in [0, w1, ]in which |L(jw)<1. The best design option depends on the specific problem. One problem class is given where the new option is preferable.

ISSN:0020-7179    

DOI:10.1080/00207178408933324

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The design of multivariable servomechanism controllers is considered here for plants whose parameters are uncertain or perturbed within a cone-bounding criterion. The solution comes from a controller design problem as an LQ optimal control problem in which the gain matrices result in a quadratic performance upper bound (similar to that described by Gilman and Rhodes (1976() which depends on the uncertainty. Under conditions on the nominal plant and on the uncertainty, a resulting linear time-invariant controller is guaranteed to achieve the objectives of robust tracking and regulation with closed-loop stability.

ISSN:0020-7179    

DOI:10.1080/00207178408933325

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Decentralized stabilization and stability domain estimation of a class of continuous and discrete non-linear interconnected systems are investigated. It is shown that the definite positive solution of a Ricatti equation allows the development of a method which gives better results (in some tested examples) than other methods specially developed to deal with non-linear systems.

ISSN:0020-7179    

DOI:10.1080/00207178408933326

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor