Modified Grey Wolf Optimizer and Application in Parameter Optimization of PI Controller

The Grey Wolf Optimizer (GWO) is a well-known metaheuristic algorithm that currently has an extremely wide range of applications. However, with the increasing demand for accuracy, its shortcomings of low exploratory and population diversity are increasingly exposed. A modified Grey Wolf Optimizer (M-GWO) is proposed to tackle these weaknesses of the GWO. The M-GWO introduces mutation operators and different location-update strategies, achieving a balance between exploration and development. The experiment validated the performance of the M-GWO using the CEC2017 benchmark function and compared the results with five other advanced metaheuristic algorithms: the Improved Grey Wolf Optimizer (IGWO), GWO, Whale Optimization Algorithm (WOA), Dung Beetle Optimizer (DBO), and Harris Hawks Optimization (HHO). The performance results indicate that the M-GWO has a better performance than competitor algorithms on all 29 functions in dimensions 30 and 50, except for function 26 in dimension 30 and function 28 in dimension 50. Compared with competitor algorithms, the proposed M-GWO is the most effective algorithm, with an overall effectiveness of 96.5%. In addition, in order to show the value of the M-GWO in the practical engineering field, the M-GWO is used to optimize the PI controller parameters of the current loop of the permanent magnet synchronous motor (PMSM) system. By designing a PI controller parameter optimization scheme based on the M-GWO, the fluctuation of the q-axis current and d-axis current of the motor is reduced. The designed scheme reduces the q-axis fluctuation to around −2~1 A and the d-axis current fluctuation to around −2~2 A. By comparing the current-tracking errors of the q-axis and d-axis under different algorithms, the validity of the optimized parameters of the M-GWO is proved.