摘要:

This paper addresses the two basic and related problems of minimal inversion and perfect output control in linear multivariable systems. A simple analytical expression is obtained for the inverse of the transfer-function matrix of a square multivariable system. This expression is then used to construct a minimal-order inverse of the system. It is shown that the poles of the minimal-order inverse are the transmission zeros of the system. As a result, necessary and sufficient conditions for existence and stability of the inverse system are stated simply in terms of the zero polynomial of the original system. Furthermore, the minimal-order inverse is shown to be proper provided the original system has a full rank feedthrough matrix. The related problem of perfect output control, namely command matching and disturbance decoupling, in linear multivariable systems by means of feedforward controllers is also formulated and solved in a transfer-function setting. It is shown that a necessary and sufficient condition for existence of the required controllers is that the plant zero polynomial is not identical to zero or unstable. The order of the required controllers is equal to the number of plant transmission zeros. The control scheme proposed in this paper is composed of a feedback controller to enhance system stability and robustness, a feedforward controller to ensure command matching, and another feedforward controller to achieve disturbance decoupling. The three controllers have no effect on each other and can therefore be designed independently. A number of numerical examples are discussed for illustration.

ISSN:0020-7179    

DOI:10.1080/00207178908559765

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The linear quadratic regulator problem is considered for discrete time systems with time delay. The theory forms a close parallel to that for stationary prediction and filtering. For coloured noise disturbance at the plant input it is shown that the optimal control decomposes into the solution for white noise disturbance plus a feedforward controller. For unit time delay the solution becomes equivalent to that given by the stationary Kalman theory.

ISSN:0020-7179    

DOI:10.1080/00207178908559766

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

An orthogonal least squares estimator, which was originally derived for single-input single-output systems, is extended to multi-input multi-output non-linear systems. The estimator can provide information about the structure, or which terms to include in the model, and final parameter estimates in a very simple and efficient manner. Multivariable non-linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included.

ISSN:0020-7179    

DOI:10.1080/00207178908559767

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A systematic design method for assigning a required time-scale structure to a given multivariable system is developed. The time-scale structure assignment is carried out using high-gain feedback of either the state or the output. The method developed decomposes a given multivariable system into several single-input single-output subsystems, each of which is designed separately. A standard method of design for single-input single-output systems is developed, and this forms a building block for the multivariable system design. The state feedback design depends only on the stage sequence of the given system, while the output feedback design depends only on the set of integers that specifies the order of infinite zeros. In this way, our design is made robust with respect to certain parameter uncertainties. High-gain parameter(s) can be adjusted on line, and this provides a tool for the fine tuning of the desired performance characteristics of a control system.

ISSN:0020-7179    

DOI:10.1080/00207178908559768

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability ofx = Axfor some appropriateA.The existence of such a Lyapunov function can be determined by solving a convex program. We present several numerical methods for these optimization problems. A simple numerical example is given.

ISSN:0020-7179    

DOI:10.1080/00207178908559769

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The problem of transfer function estimation is considered. We will discuss the problem in two (related) aspects: firstly, how to obtain a good black-box transfer function model; secondly, how to derive a suitable description of the model uncertainty (modelling errors). We will emphasize the second point. We shall discuss the asymptotic theory on the properties of transfer function estimates, developed recently by Ljung and Yuan. This new theory shows that the transfer function estimate is consistent, the error of the estimate is asymptotically normal, with a very simple expression for its variance. Their results will be extended here to cases where spectral analysis is used. Based on this theory, we will propose the method for obtaining a low-order nominal model of linear processes, and define and estimate an upper bound of the model uncertainty. An upper bound of the model uncertainty is a suitable description of the modelling errors for the robust controller design.

ISSN:0020-7179    

DOI:10.1080/00207178908559770

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The identification of measurement, parametric, and structural model uncertainty is considered for models from observations with bounded noise. A min-max estimate for the upper bound of the structural model uncertainty is presented. The propa- gation of the parametric and structural model uncertainty, as a result of the obser- vation uncertainty bounds to the model prediction error, is examined. A simple water quality model is used to illustrate the different steps.

ISSN:0020-7179    

DOI:10.1080/00207178908559771

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Jiang (1988) stated that the Schur stability of an interval matrixAIis equivalent to that of the vertices ofAI.We point out, via a counter-example, that this result is incorrect.

ISSN:0020-7179    

DOI:10.1080/00207178908559772

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

ISSN:0020-7179    

DOI:10.1080/00207178908559773

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

ISSN:0020-7179    

DOI:10.1080/00207178908559774

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor