Robust feedback compensation and PID Tuning under actuator rate limit effect based on Bode’s integrals

Abstract

The actuator rate limit is a common phenomenon in control systems while its underlying mechanism remains elusive. Magnitude reduction and phase delay generated by the rate limiter degrade the control performance, but this adverse effect has always been omitted in practical engineering. This study proposes a robust controller design method and controller update rules for general minimum-phase systems to compensate for the rate limit effect and improve control performance. Firstly, a simplified implementation method of “flat phase” constraint is carried out based on the Bode’s integrals for proportional–integral–derivative (PID) and fractional-order proportional–integral (FOPI) controllers. Secondly, the update rules of the controller design specifications are proposed based on Bode’s integrals to mitigate the actuator rate limit effect. The proposed method maintains the original controller structure without extra compensation filters, thereby can be easily applied to engineering practice. The outperformance of FOPI controllers compared to PID controllers is qualitatively analyzed and has been indicated to have lower probability of infinity loops under actuator rate limit. Illustrative examples and experimental results have demonstrated the effectiveness, robustness under gain variation and disturbance rejection capability of the proposed rate limit compensation strategies.