Design of robust fractional order PID controller using fractional weights in the mixed sensitivity problem

In this paper, a Fractional Order Weighting Matrices FOWM are introduced in the mixed sensitivity problem in order to design the proposed Fractional Order PID controller FOPID. The aim of this proposition is to enhance the trade-off between the Nominal Performances NP and the Robust Stability RS of the closed-loop system where the neglected dynamic, the unstructured model uncertainty and the effect of the sensor noises are considered. The proposed fractional controller and fractional weighting matrices parameters are simultaneously determined through solving the H
_∞
optimization problem using an adequate min-max optimization algorithm. The obtained performances are compared, in time and frequency domains, with those given by the standard fractional order PID controller where its optimization problem is given by usual Integer Order Weighting Matrices.