A novel approach based on a nonlinear compensator is prposed to prevent windup, which is caused by the saturation of the acutator and the integral action of the controller. The anti-windup compensator is located between the conventional linear controller, designed neglecting the saturation, and the actuator. It was proven based on the describing function method that, if the closed loop control systems are stable assuming no saturation, then there may exist a range of compensator gain which prevents any limit-cycle. The computer simulation results show that the compensator proposed in the manuscript can eliminate the limit cycle and improve the transient response.