Design of Robust Fractional-Order PID Controller for DC Motor Using the Adjustable Performance Weights in the Weighted-Mixed Sensitivity Problem

Abstract

This paper deals with the robust series and parallel fractional-order <em>PID</em> synthesis controllers with the automatic selection of the adjustable performance weights, which are given in the weighted-mixed sensitivity problem. The significant contribution of the paper is to achieve the good trade-off between nominal performances and robust stability for DC motor regardless its nonlinear dynamic behavior, the unstructured model uncertainties and the effect of the sensor noises on the feedback control system. The main goal is formulated as the weighted-mixed sensitivity problem with unknown adjustable performance weight. This problem is then solved using an adequate optimization algorithm and its optimal solution leads to determine simultaneously the robust fractional <em>PID</em> controller, which is proposed by the series and the parallel fractional structures, As well as, the obtained optimal solution determines the corresponding adjustable performance weight.<strong><em> </em></strong>The proposed control technique is applied on DC motor where its dynamic behavior is modeled by unstructured multiplicative model uncertainty. The obtained performances are compared in frequency- and time-domains with those given by both integer controllers such classical <em>PID</em> and <em>H<sub>∞</sub> </em>controllers.