The problem of designing a controller for a multi-vectored propeller airship with independent amplitude and rate saturations is addressed. First, a linear Proportional-Integral-Derivative (PID) controller is introduced for position control without considering the input saturations. Then, two design methods are applied to the traditional PID control output to satisfy the independent amplitude and rate constraints: the nested saturated PID controller (N-PID) and the transformed PID controller (T-PID). The bounded magnitudes and rate outputs of the modified controllers are given. Simulation results showed both controllers have good tracking performance while satisfying independent amplitude and rate saturations. However, the transformed PID controller has the advantage of expressing explicitly the relationship of the actuator magnitude and rate saturations with the parameters of the transformed function such that the actuator saturations are suppressed by calculation but not by trial and error.