Robust Anti Windup Controller Synthesis of Multivariable Discrete Systems with Actuator Saturation

This paper aims at simultaneously synthesizing a windup compensator and controller using linear matrix inequalities (LMIs). The proposed method can be applied to any multivariable (MIMO) uncertain discrete linear system with actuator saturation and any linear control structure. The controller and windup compensator design is done iteratively. Depending on the application, one of two possible optimization problems is solved to maximize either the decay rate or the domain of attraction. The stability of the closed loop is always guaranteed by using a quadratic Lyapunov function. The approach is applied to an unstable model of the F/A 18 HARV aircraft. Different types of controllers (PID, PID with windup compensator, full state feedback) are shown, as well as the effect of system uncertainties. A second example demonstrates the effectiveness and diminution of conservativeness of the proposed method, compared to another approach using parameter dependent Lyapunov functions.