Improved Gray Wolf Optimization Algorithm for Tuning Non-integer Order Proportional Integral Derivative Controller Design

In this study, a noninteger-order proportional–integral–derivative (NIOPID) controller was used for controlling the speed of the direct current (DC) motor. The controller parameters have optimally been adjusted using the GWOJOS algorithm formed by combining the Grey Wolf Optimization (GWO) algorithm and the recently defined the Joint Opposite Selection (JOS) feature. The JOS brings a mutual reinforcement by a joint of the two opposition strategies Dynamic Opposite (DO) and Selective Leading Opposition (SLO). The DO and SLO improve the balance of exploration and exploitation, respectively, in a given search space. During the optimization phase, JOS helps GWO attack the target quickly by employing SLO. DO help GWO find more opportunities to find the most suitable prey. The GWO is able to improve its performance with JOS. This combination helps accelerating the convergence rate of GWO. We assessed GWOJOS's performance using the benchmark functions from the IEEE Congress on Evolutionary Computation 2017 (CEC2017). The benchmark covers composition, hybrid, multimodal, and unimodal functions. The NIOPID-based speed control system for DC-motor using the GWOJOS algorithm has been designed using a time domain objective function that takes into account the performance criteria (maximum overshoot, steady-state error, rising time, and settling time). Some analyses, including robustness, time and frequency domain simulations, have been used to evaluate the performance of the proposed novel approach. The evaluation results have shown that the performance of GWOJOS was better than the performance of GWO, Slime Mould Algorithm (SMA), Atom Search Optimization (ASO), Simulated Annealing (SA) and the hybrid optimization algorithm created by opposition-based learning (OBL) strategy of SA and SMA algorithms (OBLSMASA).