Robust optimal fractional-order proportional-integral and proportional-derivative controller design for integrating systems with time delays: Real-time application to quadrotors

This paper proposes a robust design that relies on the use of dual-phase and gain margin testers in the inner and outer loops of fractional-order proportional-integral and proportional-derivative (FOPI-PD) controllers to increase controller robustness against disturbances. Tuning rules are provided to calibrate FOPI-PD based on the proposed design method. Furthermore, an optimal design for the controller parameters computed by the tuning rules is suggested using a coati optimization algorithm (COA), constrained by the robust stability region to accelerate the optimization process. Here, the exploitation stage of the COA is redesigned to be suitable for searching positive domains. In addition, Oustaloup’s parameters for approximating the fractional terms of the controller are simultaneously designed using COA along with the controller parameters to improve the tracking capabilities of the controller. The results show an improvement of at least 10° in the phase margin using the proposed method relative to PI-PD based on a single-phase and gain margin tester. The findings obtained using simulations and real-time evaluations show that all the studied cases exhibit significantly improved resistance to parameter changes and disturbances compared with the current approaches.