Gain-scheduled anti-windup PID control for LPV systems under actuator saturation and its application to aircraft

To fill in the gap between theory and practice, this paper presents a gain-scheduled anti-windup proportional-integral-derivative (PID) control strategy for linear parameter-varying (LPV) systems with actuator saturation. Using the relationship between saturation and deadzone nonlinearities, the resulting closed-loop system is recast into a system with a deadzone nonlinearity. With the aid of a parameter-dependent sector condition, the stability and ℒ_2 performance of the closed-loop system are elaborated using parameter-dependent Lyapunov approach. The developed synthesis condition is first formulated in terms of bilinear matrix inequalities (BMIs), which cannot be easily solved. Then, a set of linear matrix inequalities (LMIs) is derived by employing Finsler’s lemma. Finally, the proposed control strategy is applied to the flight control design of a lateral-directional aircraft system to illustrate its effectiveness and application potential.