An enhanced hybrid stochastic fractal search FOPID for speed control of DC motor

We combine the stochastic fractal search (SFS) and pattern search optimization technique to create a hybrid stochastic fractal search (HSFS) algorithm, which is integrated with fractional-order-proportional-integral-derivative (FOPID) controller for controlling the celerity of the DC motor. For optimal speed control, the FOPID controller parameters are optimized by the HSFS algorithm using the minimization of objective function (OF), the integral time multiplied absolute error (ITAE). The proposed HSFS algorithm to optimize the FOPID parameters for controlling the same is called the HSFS-FOPID approach. SFS is a metaheuristic algorithm incentivized by the concept of fractal, and FOPID is flexible in controlling higher-order systems. The particle in this algorithm explores the search space more efficiently by using the diffusion property which is present in an arbitrary fractal. Present work uses the properties of both methods and controls the designed DC motor. The excellence of the proposed approach HSFS-FOPID for the aforesaid DC motor is demonstrated by comparing the results with popular approaches in the existing literature. The comparison results reveal better performance of HSFS-FOPID for the aforesaid DC motor while comparing with existing techniques in terms of overshoot, settling time, rise time, and ITAE.