摘要:

A model reduction problem (MRP) is related to the control problem by use of a ‘ model quality index ’ which measures the performance of the higher-order system when the control is based upon a lower-order model. By truncating modal coordinates which have smaller sensitivity to the model quality index a first approximation to the MRP is obtained. Another approximation to the MRP is obtained by truncation of modal coordinates which have smaller sensitivities to the first term in the model quality index, called the ‘ cost of information ’. Several theorems relate the scalar measures of observability of each modal coordinate to the first-order sensitivity of the ‘ cost of information ’ and of the model quality index. A case study with a flexible spacecraft illustrates truncation on the basis of observability measures and controllability measures.

ISSN:0020-7179    

DOI:10.1080/00207177908922719

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The stability of time delay systems incorporating a Smith controller is discussed. It is shown that a system, which gives optimum response for perfect matching of the plant model and plant, may become unstable if a mismatch occurs. The stability boundaries are given for variations in gain, time constant and time delay of models and plant having the general form

ISSN:0020-7179    

DOI:10.1080/00207177908922720

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

Certain connections between the geometric theory of Wonham and Morse and the Rosenbrock— Wolovich—Forney polynomial matrix approaches to linear system theory are indicated. The results of Warren and Eckberg (1975), worked by Vardulakis (1977) into an algorithm which constructively exhibits all controllability subspaces of a given controllable pair (A, B) in canonical form, are extended and turned into a theoretical tool of considerable power. A new theory is developed which translates certain statements of the geometric theory into a succinct algebraic form

ISSN:0020-7179    

DOI:10.1080/00207177908922721

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

In the light of the concept of a decoupling vector (Stoyle and Vardulakis 19797rpar; as a minimal algebraic parametrization of a controllability subspace (c.s), the mechanism of decoupling control by state feedback is investigated. The essential equivalence of the Wonham and Morse (1970) and Falb and Wolovich (1969) solutions of the diagonal non-block restricted decoupling problem (BDP) might well be suspected and the method of decoupling vectors intertwines these so that each is seen to be crucial to the efficient formulation and solution of decoupling problems. A new formula for the classical necessary and sufficient condition given by Falb and Wolovich (1967) in terms of their B* matrix emerges naturally from the analysis. The role of decoupling c.s.s in the guise of their associated and very easily obtained decoupling vectors in solving BDP for us becomes very clear. The solution given leads to the important definition of cyclic independence for c.s.s and this is relevant to reducing other types of decoupling problems to the basic case above

ISSN:0020-7179    

DOI:10.1080/00207177908922722

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The transfer function representation of controllers designed by modern state-variable design methods is considered. It is shown that procedures currently being used to design state feedback control laws and state observers (state filters) do not guarantee that the overall controller will be stable. In this paper, additional criteria which do guarantee stable controllers are derived for a general class of second- and third-order systems. A numerical example is presented.

ISSN:0020-7179    

DOI:10.1080/00207177908922723

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

This paper describes the refined IVAML algorithm for estimating the parameters in the multivariable analogue of the single input,. single output model considered in Part I. It also shows that similar refined algorithms can be constructed for other multivariable model forms, including the ARMAX, dynamic adjustment (DA) with autoregressive errors and the multivariable transfer function (MTF). The performance of the algorithm is evaluated by Monte Carlo analysis applied to four simulation models with between 25 and 39 parameters and it is carried out for various sample sizes and signal/noise ratios. As in the SISO model version, the analysis indicates that the algorithm yields asymptotically efficient estimation results, whilst providing low variance estimates of the basic system parameters for medium sample sizes.

ISSN:0020-7179    

DOI:10.1080/00207177908922724

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

There is given a single input-output linear, time-invariant plant with large parameter uncertainty consisting of two parallel branches, one of which has n internal sensing points. The objective is to satisfy specified frequency domain bounds on the system response to commands and disturbances over the parameter range, and to do so with sensibly minimum net effect at the plant input, of the n + 1 sensor noise sources. The basic problem is how to best divide the feedback burden among the n + 1 available feedback loops Li. The procedure developed has high transparency, giving early perspective on the loop bandwidths, permitting approximate loop trade-offs without a detailed design. While the development is more difficult than in the single cascaded plant system, the procedure and final results are very similar : each Lihas only one distinct frequency range say ωi, in which there is trade-off between Liand LI+1and ωii+1<ωiwith steadily increasing loop bandwidths going backwards from plant output to input. It is shown that for a class of problems the sensor noise can be tremendously reduced, when compared to an optimum single-loop design satisfying the same specifications.

ISSN:0020-7179    

DOI:10.1080/00207177908922725

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

The purpose of this paper is to indicate how characteristic gain loci(or generalized Nyquist diagrams) can be used to count the number of characteristic frequencies (or closed-loop poles) which occur in a given area of the frequency plane for any given feedback gain. The relationship between the gain loci and the characteristic frequency loci is shown to hold for a wide range of linear systems, both sampled and continuous, including those with time delays. The relationship between the frequency loci and the inverse gain loci (or inverse Nyquist diagrams) is also deduced. These results are then used to show how for many systems the frequency loci can be used to determine the only possible ranges of feedback gain to obtain a stable closed-loop system. It is also indicated why in many real systems the closed-loop system should be stable at all but the edges of these possible ranges of feedback gain. The approach used avoids the complex integration which is usually used to justify the Nyquist diagrams (Bode 1945). One example demonstrating the superiority of state-space models over rational polynomial Laplace transfer-function models in the determination of the stability of multivariable systems is given. Some examples of gain loci, inverse gain loci, frequency loci and inverse frequency loci for systems with and without time delays are included.

ISSN:0020-7179    

DOI:10.1080/00207177908922726

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor

摘要:

In this note, a class of well-known canonical forms for linear controllable and observable systems are extended to bilinear systems. It is shown that, unlike the linear case, the canonical forms are not, in general, unique even if the system is single-terminal, not to mention multi-terminal.

ISSN:0020-7179    

DOI:10.1080/00207177908922727

出版商:Taylor & Francis Group    

年代:1979

数据来源: Taylor