Optimal anti-windup control of saturating discrete-time MIMO systems

Directional changes in control signals due to actuator saturation may cause severe deterioration in performance, especially when a plant is ill-conditioned. However, this fact is usually ignored by conventional anti-windup schemes. To tackle this problem, this paper presents an anti-windup controller that provides graceful degradation of closed-loop performance for saturating discrete-time MIMO systems. In addition, linear performance is preserved in the absence of actuator saturation. 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 served 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 in the illustrative example.