## 1 Introduction  
The PMSM is becoming increasingly widespread in industrial manufacturing due to its many advantages over other types of motors [1]. Many high-precision and high-performance control methods for the PMSM have been widely developed and applied, including PI control [2; 3], adaptive control [4; 5], Sliding Mode Control (SMC) [6; 7], \(H_{\infty}\) control [8; 9], model-referenced adaptation [10; 11], and Internal Model Control (IMC) [12; 13]. Despite the widespread usage of PI control, it is challenging to obtain an optimal performance because PI controllers are highly dependent on parameters that are challenging to adjust in a disruptive and changing work environment. Adaptive control is governed by complicated laws. Conventional SMOs introduce high-frequency jitter due to the reference of discontinuous switching functions, and the use of a low-pass filter to filter out the high-frequency jitter means the estimated position is always delayed from the actual position. The application of these control techniques is constrained as a result of these issues. In recent years, ADRC proposed by Prof. [PERSON] has been applied in the PMSM speed servo system [14; 15; 16]. It mainly consists of a Tracking Differentiator (TD), an Extended State Observer (ESO), and the Nonlinear State Error Feedback (NLSEF) control law [17]. The core of ADRC is the ESO. The ESO employs two parameter values to estimate the rotor speed and disturbance states of the system, with particular emphasis on estimating the total perturbation. This estimation ultimately impacts the control effectiveness. NLSEF, as a component of the ADRC algorithm, demonstrates superior response efficiency when compared to the linear control rate. The primary purpose of TD is to facilitate a transition process that minimizes overshooting [14]. Furthermore, ADRC has been enhanced through the application of various intelligent control algorithms. In [18], an improved ADRC with ESO and finite-time stable TD was applied to the flexion-extension motion of the shoulder joint and the elbow joint. The method focuses on tracking accurate motion trajectories and reducing trajectory tracking errors to improve the tracking accuracy of the system and enhance the robustness of the controller to internal parameter uncertainties. In a previous study [19], a measurement delay-compensated linear ADRC method is proposed. This linear ADRC-based method addresses parameter perturbations, dead time nonlinearities, and unmodeled uncertainties to ensure system immunity performance. A previous study [20] introduced a hybrid control algorithm that combines Backpropagation Neural Network (BPNN)-based ADRC with adaptive fuzzy SMC. This approach combines fuzzy SMC with BPNN-based ADRC, eliminating the tuning blind zone and enhancing the system's anti-interference capacity, while also ensuring system adaptability. A parameter tuning method for ADRC using a Genetic Algorithm (GA) was proposed in reference [21]. According to experimental results, GA can handle difficult problems that are beyond the capabilities of conventional empirical techniques and demonstrates superior performance in adjusting the parameters of stabilized systems. In these improved ADRC algorithms, a single ESO is assigned the task of estimating and compensating for the total disturbance, leading to an increased burden on the ESO. To ensure precise estimation, the ESO must choose a substantial gain, which can potentially trigger system instability and vibration [22]. In [23], a load-adaptive dual-loop drive system for a robotic arm joint is described. This system utilizes an improved ADRC that integrates the position and velocity of the motor rotor and introduces a Fuzzy Controller (FC) for parameter tuning. This method can alleviate the burden of ESO prediction and adjustment to some extent. In a particular study [24], a dynamic parameter tuning method for ADRC is described, which involves the combination of GA and BPNN. GA is used to optimize the initial value of the BPNN to achieve real-time tuning of ADRC parameters.