Multivariable Robust Proportional-Integral-Derivative Control for Linear Quadratic Compensation of a Class of Norm-Bounded Uncertain Systems

Abstract

This paper is concerned with designing multi-input multi-output (MIMO) proportional-integral-derivative (PID) control having filtered derivative terms to achieve optimal linear quadratic performance for a class of linear uncertain MIMO systems with norm-bounded time-varying uncertainties. A necessary and sufficient condition for existence of the PID controller is obtained in terms of rank constrained linear matrix inequalities (LMIs). Using an existing penalty-function-based approximation for matrix rank minimization, an algorithm is proposed to solve these rank constrained LMIs and find PID gains. A suitable numerical example is considered to show the efficacy of the proposed approach in ensuring robust performance as compared to the existing ones. The proposed algorithm is also tested on several benchmark examples and found to be computationally much more efficient than some well-known methods.