The effect of actuator saturation on the performance of PD-controlled servo systems

Abstract Perhaps the most often utilized means of closed-loop control of a servo system is proportional-derivative (PD) control. Linear analysis methods suggest the best tracking performance is achieved at maximum possible proportional and derivative gains. Maximum gains, however, drive the actuators into saturation, which renders the system nonlinear and the linear analysis invalid. This paper investigates the effect of actuator saturation on servo system tracking performance by formulating a frequency-based tracking performance measure roughly equivalent to the linear system −3 dB bandwidth. The proposed measure utilizes a series of band-limited pseudo-random tracking inputs to characterize the ‘bandwidth’ of the (nonlinear) saturating system. Numerical simulations based on this measure show that, for a servo system that exhibits actuator saturation, the best tracking performance is not achieved at maximum gain. Instead, performance improves up to a given gain, then begins to recede as the gain is increased further. The simulations also show that avoiding actuator saturation to ensure linear behavior significantly sacrifices tracking performance. The measure of tracking performance is compared with the −3 dB bandwidth utilized in linear analysis techniques, and the two are shown to be well correlated.

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