## 1 Introduction  
Power electronics is rising dramatically at the present time, and permanent-magnet synchronous motors (PMSMs) have come to be widely used in robotics, electric vehicles, the aerospace industry, and other fields owing to their compact structure, high torque-to-current ratio, and efficiency, as well as their power density and fault tolerance [1, 2]. As the innermost loop of the three-loop cascade system of current, speed, and position, the current loop plays a crucial role [3]. Therefore, a lot of studies have proposed methods to optimize current control, such as using proportional integral (PI) control, sliding mode control (SMC), and predictive control, amongst others [4, 5, 6, 7]. PI control has been widely used because of its simple structure, simple arithmetic, and easy implementation, but in fact, PMSM control systems are nonlinear, and this method is a linear control algorithm, so it cannot guarantee that the response speed and accuracy will be balanced simultaneously [4, 5]. SMC has low sensitivity to parameter variations and disturbances, and it is highly robust. However, discrete control may cause chattering, which decreases the control performance [6]. With the progress of discrete digital control technology and the constant optimization of chip-processing capabilities, predictive control has attracted considerable attention and has been widely researched due to its simple structure and better dynamic performance. Predictive control methods can be classified as deadbeat predictive control (DPC), trajectory predictive control, model predictive control (MPC) [7], etc. The dynamic performance and control precision of DPCC is excellent, and DPCC, which has a fixed switching frequency and requires only simple computation compared with other current predictive control methods, can be used in combination with space vector pulse-width modulation (SVPWM) to input to the inverter; hence, it is used widely [8]. However, DPCC is sensitive to parameters, and its control performance is associated with the motor parameters in the prediction model. Temperature variations, magnetic saturation, cross coupling [9], and other disturbances lead to motor parameter mismatches, which result in steady-state errors in DPCC, and this is detrimental to the performance of the control. The available optimization methods that can be used to solve the abovementioned problems associated with DPCC include the model-free control method, parameter identification, disturbance observer compensation, etc. In [8], model-free control combined with a Luenberger disturbance observer is proposed to improve DPCC performance. This proposed method compensates the error by calculating the predictive control voltage and combining the estimated total disturbance with the ultra-local model. In [10], a parameter decoupling identification method is suggested to decouple and reduce the mutual influence between the stator inductance and the flux linkage, and it is optimized using the Kalman algorithm, which is effective in reducing the current steady-state error and harmonic content. In [11], a control method for the online updating of internal relevant parameters is suggested. This method uses an extended Kalman filter to filter the current, which is effective and easily implemented. In [12], a modified reaching law combined with a non-singular terminal sliding mode disturbance observer is used for compensation, and a harmonic compensation term is added to the current control output, which compensates the error and enhances the robustness of the system. In [13], voltage compensation and the elimination of steady-state error are achieved by improving the non-homogeneous disturbance observer, and a power reaching law is designed to make the system converge better. Some researchers have also achieved a boost by improving both the current and the speed loops. In [14], a speed sliding mode controller is designed to enhance the interference immunity while introducing a reaching law to compensate for the DPCC error.