Abstract
The preview control problem of a class of linear discrete-time descriptor systems is studied. Firstly, the descriptor system is decomposed into a normal system and an algebraic equation by the method of the constrained equivalent transformation. Secondly, by applying the first-order forward difference operator to the state equation, combined with the error equation, the error system is obtained. The tracking problem is transformed into the optimal preview control problem of the error system. Finally, the optimal controller of the error system is obtained by using the related results and the optimal preview controller of the original system is gained. In this paper, we propose a numerical simulation method for descriptor systems. The method does not depend on the restricted equivalent transformation.
Highlights
Preview control theory takes full advantage of future known reference signals or disturbance signals information to improve the dynamic response, to inhibit the disturbance, and to increase the tracking performance of the systems
The tracking problem is transformed into the optimal preview control problem of the error system
The optimal controller of the error system is obtained by using the related results and the optimal preview controller of the original system is gained
Summary
Preview control theory takes full advantage of future known reference signals or disturbance signals information to improve the dynamic response, to inhibit the disturbance, and to increase the tracking performance of the systems. In [3], for the linear discrete-time system with previewable reference signal and disturbance signal, the augmented error system is constructed by using the difference operator and the preview controller is designed. In [4], the augmented error system is constructed to solve the problem of designing preview controller for the continuous time system. In [5], the unified algorithm of linear system and H∞ preview control problem is presented by using the Hamiltonian matrix method, which is suitable for both continuous and discrete-time systems. The optimal preview control problem for discrete-time descriptor systems, with both reference signal and disturbance signal known, is studied. The optimal regulator for the error system is obtained, and as a result, the optimal preview controller for the original descriptor system is gained. The main contribution in this paper is to design a more general simulation method for descriptor systems
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