Lower order controller design using weighted singular perturbation approximation

Authors: MUHAMMAD RAEES FURQUAN AZHAR, UMAIR ZULFIQAR, MUWAHIDA LIAQUAT

Abstract: Most of the analytical design procedures yield controllers of almost the same order as that of the plant. Resultantly, if the plant is of a high order, the controller obtained from these design procedures is also of a high order. The order of the controller should be practically acceptable for easy implementation. There are two indirect methods for designing a low order controller for high order plants: plant reduction and compensator reduction. In compensator reduction, the order of the controller designed for the original higher order plant is reduced. In plant reduction, the order of the plant is reduced for designing a lower order controller. The order of the controller or plant is reduced using model order reduction techniques. In this paper, we propose a hybrid algorithm (plant-compensator reduction) based on frequency-weighted singular perturbation approximation, which gives an improved performance as compared to existing algorithms. The proposed hybrid technique can be used with $H_{\infty}$, LQG, or any other loop shaping procedures to obtain a lower order controller. The proposed technique is validated on benchmark control problems.

Keywords: Controller reduction, input spectrum, plant reduction, singular perturbation approximation

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