One of the undesirable nonlinear phenomena in feedback control systems is called wind up, which is characterized by large overshoot, slow response, and even instability. It is caused by interaction between the integrator in the controller and the saturating actuator. Limit cycle and jump resonance are another nonlinear characteristrics of systems with saturating actuators. Several anti-windup compensators have been developed to prevent some of the aforementioned nonlinear characteristics such as instability and limit cycle, but none has studied the effect of anti-windup compensator on the jump resonance. In this paper, we developed an analytical method to design the compensator to prevent not only limit cycle but also jump resonance. An illustrative example is included to show the compensator eliminates jump resonance effectively.