Design of decoupling Smith control for multivariable system with time delays

Abstract

In order to solve the decoupling control problem of multivariable system with time delays, a new decoupling Smith control method for multivariable system with time delays was proposed. Firstly, the decoupler based on the adjoint matrix of the multivariable system model with time delays was introduced, and the decoupled models were reduced to first-order plus time delay models by analyzing the amplitude-frequency and phase-frequency characteristics. Secondly, according to the closed-loop characteristic equation of Smith predictor structure, proportion integration (PI) controllers were designed following the principle of pole assignment for Butterworth filter. Finally, using small-gain theorem and Nyquist stability criterion, sufficient and necessary conditions for robust stability were analyzed with multiplicative uncertainties, which could be encountered frequently in practice. The result shows that the method proposed has superiority for response speed and load disturbance rejection performance.

Keywords

multivariable process / time delay / Smith predictor / decoupling / robust stability