Internal Model Control for Singular Multivariable Systems Based on Kronecker Canonical Form

Abstract

Abstract-The internal model control design method for stable plants has enjoyed much popularity due to its simple yet effective procedure. In this paper, a robust IMC method is proposed for multivariate singular systems on the basis of Kronecker canonical form, which allows us to analysis and control of a singular linear system conveniently. Instead of considering the state space approach, the proposed procedure is derived on the basis of transfer function matrix. Based on this equivalent restrict decomposition form, the control object is first decomposed into separate slow and fast subsystems of lower dimensions and permitted a simple design. Then a feed forward controller is designed to eliminate impulse for fast subsystem, followed by that an internal model controller is designed for slow subsystem. For ease of implementation's sake, time-scale transformation is introduced. The proposed method is also verified applicable for impulse-free singular systems. In order to improve control precisions, the diagonal filter is designed with Genetic algorithms. During the optimization process, the integral of squared error index is adopted. Simulation results demonstrate the validity of the proposed approaches.