Saturation is one of the non-linearities, which most actuators in actual control systems have. In case that the controller includes more than one pure integrator, integral windup can occur. Large over-shoot and limit cycle, which is a non-linear phenominon having the system oscillating with constant frequency and constant amplitude, are typical indicators of the windup.
To avoid windup, most of the past researches constrainted on development of the new controller which stabilized the closed-loop system and avoided any limit-cycle. Recently a novel approach was proposed to prevent windup, which didn't replace the linear controller designed neglecting the saturation, but located an anti-windup compensator between the controller and the actuator.
In this paper, a structural scheme of a generalized anti-windup compensator applicable to a MIMO system is proposed, and it is shown that this scheme is proper by analyzing the stability in the linear and the nonlinear region of the actuator. The range of the compensator's gain, which stabilizes the non-linear closed-loop system, is calculated based on the describing function method to determine the existance of limit-cycle. Computer simulations show that the proposed compensator makes the non-linear system stable.
