A modified aquila optimizer with wide plant adaptability for the tuning of optimal fractional proportional-integral-derivative controller

The heuristic tuning method of fractional-order proportional-integral-derivative (FOPID) control systems lacks robustness, and its performance often changes with specific controlled plants. To solve this problem, this paper proposes a new modified aquila optimizer for tuning the parameters of the FOPID controller, which has strong plant adaptability and can be applied to a large class of different controlled plants. A series of new operational mechanisms, including Tent map-based initialization, probability-based dynamic update, greedy-based Gauss mutation, a fully random search strategy with uniform distribution, and the wraparound dynamic weight update for local exploitation, are proposed to tackle the existing problems of the classical aquila optimizer, such as slow convergence, low precision, and local optimum. Standard benchmark functions are used to test the proposed modified aquila optimizer, showing superior performance in terms of convergence speed, precision, and robustness. The Wilcoxon and Friedman tests statistically proved the significant difference of the modified aquila optimizer from other competitors. Five control system cases with different plants further validate the effectiveness, feasibility, wide adaptability, and superiority of the proposed modified aquila optimizer for regulating FOPID controller parameters. It is approved that the proposed modified aquila optimizer with new mechanisms has wide plant adaptability, deeming a good prospect for the tuning of optimal FOPID controller.