One of the undesirable nonlinear phenomenon called 'wind up' occours when the integrator in the controller and the saturated actuator interact. Large overshoot, slow response, instability, limit cycle and jump resonance are the characteristics of wind up phenomenon. Several 'anti-windup' compensators have been developed to prevent some of the aforementioned nonlinear characteristics such as instabilituy and limit cycle, but none has studied the effect of antiwindup compensator on the jump resonance. In this paper, we developed an analyitcal 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 of effectively.