摘要:

A left (right) block modal matrix is constructed to decompose a class of linear time-invariant MIMO state equations in arbitrary co-ordinates into a block diagonal canonical form which contains left (right) solvents of a characteristic polynomial matrix. The applications of block modal matrices to block partial fraction expansions, analytical time-response solutions, and model reductions of high-degree matrix fraction descriptions and high-order state equations are examined. Also, the relationship between a left (right) solvent of a matrix polynomial and the corresponding right (left)solvent is explored. The established block canonical forms in the time domain, and developed algebraic theories, provide additional mathematical tools for the analysis and synthesis of a class of MIMO control systems and matrix functions.

DOI:10.1049/ip-d.1982.0010

出版商:IEE    

年代:1982

数据来源: IET

摘要:

Approximate feedback design of a class of singularly perturbed linear regulators is developed. Two perturbation parameters are introduced, in particular, to account for the degree of smallness and extent of largeness of two boundary modes with respect to the normal mode of operation. An approximation is employed to separate the overall design into three regions. An index of suboptimality is also derived. A 9th order example is worked out to illustrate the theoretical analysis.

DOI:10.1049/ip-d.1982.0011

出版商:IEE    

年代:1982

数据来源: IET

摘要:

The problem of controller design for an unknown discrete or continuous multivariable system in the frequency domain based on open-loop step-response data alone is considered. The approach is based on the use of simple approximate plant models possessing the property that the resulting error in modelling the plant open-loop step response is both monotonic and sign-definite as a function of time. In such circumstances, the frequency-domain properties of the approximating feedback system and the error involved in predicting steady-state characteristics are sufficient data to predict the stability of the real feedback system. If integral controller elements are included, the results also provide sufficient conditions for exact tracking of step demands. Under certain circumstances, the technique has strong connections with the well known inverse Nyquist array design method and can be regarded in part as a modification and generalisation of that techniqiue to cope with unknown interaction dynamics.

DOI:10.1049/ip-d.1982.0012

出版商:IEE    

年代:1982

数据来源: IET