A fractional order proportional and derivative (FOPD) controller tuning algorithm

In recent years, it is remarkable to see the increasing number of studies related to the theory and application of fractional order controller (FOC), especially PI^λD^μ controller, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods for fractional order controllers as an extension of classical control theory. In this paper, a new tuning method for fractional order proportional and derivative (PD^μ) or FOPD controller is proposed for a class of typical second-order plants. The tuned PD^μ controller can ensure that the given gain crossover frequency and phase margin are fulfilled, and furthermore the phase derivative w. r. t. the frequency is zero, i.e., phase Bode plot is flat, at the given gain crossover frequency so that the closed-loop system is robust to gain variations and the step response exhibits an iso-damping property. The FOC design method proposed in the paper is practical and simple to apply. Simulation results show that the closed-loop system can achieve favorable dynamic performance and robustness.