An optimal anti-windup scheme for saturating MIMO systems

Directional changes in control signals due to actuator saturation may cause severe deterioration in the performance, especially when the plant is ill-conditioned. To tackle this problem, this paper presents an anti-windup controller which provides graceful degradation of closed-loop performance for saturating discrete-time MIMO systems. The present anti-windup scheme achieves its goals by minimizing the euclidean norm of the weighted difference between the performance of the saturating system and that of the unsaturated linear system. This optimal performance problem is solved under a renewed generalized conditioning technique. Necessary and sufficient conditions for the existence of a unique optimal solution and the unique optimal anti-windup control law are obtained. Stability of the saturating system is also discussed. Finally, the proposed controller is successfully applied to an uncertain ill-conditioned distillation column.