General robustness analysis and robust fractional‐order PD controller design for fractional‐order plants

Most of the existing controller tuning methods are based on accurate system model and sensitive to some inevitable uncertainties and unmeasurable disturbance. Aiming at this problem, a thorough robustness analysis on a typical kind of fractional-order (FO) delay system has been made in this study. A kind of robust FO proportional and derivative controller is proposed based on phase and gain margins. The tuning methods are demonstrated under different circumstances, namely there is gain variation, time constant variation, order variation or even multiple parameters variations in system transfer function. Simulation results show that the closed-loop control system with the proposed controller can achieve both robustness and satisfactory dynamic performance, and outperform the conventional proportional-integral-derivative controller in all cases.