I. Introduction
Permanent Magnet Synchronous Motors (PMSM) are extensively utilized across various industries owing to their benefits of easy control, superior efficiency, and improved performance[l]. Currently, PMSM control is primarily divided into direct torque control and vector control technology[2]. Due to the possibility of distortion via direct torque control, vector control is widely adopted. Nevertheless, regardless of the motor control technique, Proportional Integral (PI) control is the most widely applied and developed method in the industry due to its favorable control outcomes and low computational requirements[3]. Although the development of control theory has helped mitigate numerous drawbacks of traditional PI control (such as poor adaptive performance and complicated parameter calibration), PMSM's complex, nonlinear, and time-varying nature leads to enduring complications [4]. Thus, researchers have devoted considerable efforts to the control of PMSM. Literature [4] investigates fuzzy PI control, highlighting shorter adjustment time and reduced PMSM system overshoot. Literature [5] proposes sliding mode control in place of the conventional PI approach, delivering improved tracking performance, and dynamic response speed. The literature [6] introduces an online trained NN-PI (Neural Network Proportional-Integral) speed controller for an internal permanent magnet synchronous motor (IPMSM) drive based on SVM - DTC (Space Vector Modulation-Direct Torque Control). The system performance is improved, and overshoot is reduced. The literature[7] proposes a reduced-order sliding mode controller based on a sliding mode observer. External disturbances are considered in the controller design, and experimental results confirm the effectiveness of the controller and observer. Other literature implements neural network control and so forth[8].