New algorithm for the design of robust PI controller for plants with parametric uncertainty

Abstract

This paper proposes a new algorithm for the design of robust PI controller for plants with parametric uncertainty using new necessary and sufficient stability conditions. Most of the control systems operate under large uncertainty causing degradation of system performance and destabilization. In order to compensate these shortcomings, a robust PI controller is designed based on new necessary and sufficient conditions for stability of a plant with parametric uncertainty, a class of interval polynomial. New necessary and sufficient conditions for the determination of robust stability of interval polynomials have been developed using the results of Routhe’s theorem and Karitonov theorem. A set of inequalities are derived based on these developed new necessary and sufficient conditions to obtain robust controller parameters. The proposed method is simple and involves less computational complexity compared with the available methods in the literature. The efficacy of the proposed methodology is demonstrated with a numerical example for successful implementation.