In this paper, the closed loop speed controller parameters are optimized for the permanent magnet synchronous motor (PMSM) drive on the basis of the indirect field-oriented control (IFOC) technique. In this derive system under study, the speed and current controllers are implemented using the fractional order proportional, integral, and derivative (FOPID) controlling technique. FOPID is considered as efficient techniques for ripple minimization. The hybrid grey wolf optimizer (HGWO) is applied to obtain the optimal controllers in case of implementing conventional PID as well as FOPID controllers in the derive system. The optimal controller parameters tend to enhance the drive response as ripple content in speed and current, either during steady state time or transient time. The drive system is modeled and tested under various operating condition of load torque and speed. Finally, the performance for PID and FOPID are evaluated and compared within MATLAB/Simulink environment. The results attain the efficacy of the operating performance with the FOPID controller. The result shows a fast response and reduction of ripples in the torque and the current.