Robust PID Control with Anti-Windup Compensation for ULDS

Abstract

This paper presents an approach for the synthesis of robust PID controllers with compensation Anti-Windup (AW) for Uncertain Linear Descriptor Systems (ULDS). In a first stage, the ULDS are considered to pose parametric uncertainties of polytopic type and disturbances, as parametric variation and actuator saturation. From a condition of existence of a linear injective application, representing the generalized inverse matrix of $$\mathbb {E}$$ , the original ULDS is transformed to a linear parameter variable (LPV) system. Then, the synthesis of the robust multivariable PID controller by static output feedback (SOF) is obtained considering performance indices in $$\mathscr {H}_\infty $$ , described as linear matrix inequalities, LMIs. The PID controllers are designed without taking into account the physical restrictions of the actuators. In a second stage, taking into account the actuator saturation, an AW gain compensation is designed, which consider a performance index that involves the difference between the actuator output signal and the controller output and its effect on the control signal, then, the closed loop performance and the changes in the saturation limits of the actuators are evaluated. The minimization of the $$\mathscr {H}_\infty $$ norm is considered, which are described as a convex optimization problem of the involved transfer functions, in conjunction with the specification of closed loop performance in the absence of saturation. Performance of the proposed synthesis technique is illustrated by numerical example.