An indirect optimization scheme for tuning a fractional order PI controller using extremum seeking

The increasing amount of researches have proven the advantages of fractional order PID controllers. For fractional order PI (FO-PI) controller, the classical tuning approach is based on specifying a certain gain crossover frequency, a phase margin and a robustness to plants gain variations, it can be implemented by applying a series of open-loop experiments without an accurate process model. Additionally, the performance optimization is a widely used auto-tuning method, it searches online for the controller parameters that minimize a cost function which quantifies the closed-loop performance. Based on extremum seeking (ES) algorithm, a novel indirect optimization scheme for tuning a FO-PI controller which combines the regular ES optimization with the classical tuning approach is proposed in this paper. Instead of optimizing the controller parameters directly, we parametrize all the controllers leading to the given performance specifications (cross-over freq, phase margin, iso-damping) and then do the optimization of the cross-over freq and phase margin to achieve the best step-response performance. Simulation and experimental results demonstrate that the proposed ES optimization scheme can achieve a great balance between robustness and performance.