In this paper, we propose a design method of a nonlinear optimal controller for systems with rate limited actuators which are known to cause PIO of an aircraft. The PIO prevention problem is solved as a robust stabilization problem of a servo system for pilot commands. Simulation results demonstrate that the nonlinear controller achieves faster tracking performance with less oscillation and smaller input compared with an anti-windup compensator using the H∞ method. Robustness against parameter error, observation noise and time-delay is also confirmed.