Robust Fixed Low-Order Controller for Uncertain Decoupled MIMO Systems

The design of a robust fixed low-order controller for uncertain decoupled multi-input multi-output (MIMO) systems is proposed in this paper. The simplified decoupling is used as a decoupling system technique. In this work, the real system behavior is described by a linear model with parametric uncertainties. The main objective of the control law is to satisfy, in presence of model uncertainties, some step response performances such as the settling time and the overshoot. The controller parameters are obtained by resolving a min-max nonconvex optimization problem. The resolution of this kind of problems using standard methods can generate a local solution. Thus, we propose, in this paper, the use of the generalized geometric programming (GGP) which is a global optimization method. Simulation results and a comparison study between the presented approach, a proportional integral (PI) controller, and a local optimization method are given in order to shed light the efficiency of the proposed controller.