## 5 Conclusions  
This study focuses on the application of high-performance MPTC for PMSMs in electric vehicles, beginning with FCS-MPTC. It addresses issues such as large flux and torque fluctuations [1], difficulty in unifying physical dimensions, the need for extensive testing of weight coefficients, complex system algorithms, and the high online computation load. Strategies IMPTC, IMPTC-I, and IMPTC-II are proposed to optimize the weight coefficients, simplify the computation, and suppress the torque and flux fluctuations, enhancing the MPTC system's performance and verifying these strategies through simulations. The main conclusions are as follows. (1) To tackle the robustness issues of traditional MPTC strategies and the susceptibility to internal disturbances and external load changes, this study investigates the use of an ESO for disturbance compensation in MPTC, known as IMPTC-I. By redesigning the nonlinear error feedback function of the ESO and introducing SMC to eliminate the chattering phenomenon, a robust ESO-SMC controller with strong disturbance rejection capabilities is achieved. Additionally, two-step computation and an improved Euler formula are used for complete the delay compensation, ensuring real-time control system performance. The simulation results indicate that the proposed IMPTC-I scheme exhibits good robustness and effectively suppresses internal and external disturbances. (2) Although IMPTC-I addresses the robustness issue, it does not significantly improve the problems of the high computation load and large torque and flux pulsations. Each sampling period still requires the calculation of eight voltage vectors to find the optimal vector that minimizes the cost function, and the weight coefficients need extensive, cumbersome testing for refinement, lacking rapid and accurate selection theory and formulas. Therefore, this study, building on IMPTC-I, explores value functions and voltage vector sector diagrams, known as IMPTC-II. A new two-dimensional lookup table is designed, re  
Figure 13: Dynamic performance of IMPTC–II under parameter mismatch. quiring only two effective voltage vectors and one zero vector per cycle to find the optimal vector that minimizes the cost function, and the voltage vector sector diagram is redefined to reduce the computation while increasing the number of candidate voltage vectors. Furthermore, by analyzing the internal relationships between the electromagnetic torque, the stator flux reference values, and the angle between stator and rotor flux, a value function containing only the torque angle error terms and information about the electromagnetic torque and stator flux reference values is designed. The simulation results show that the proposed IMPTC-II scheme not only has good robustness but also demonstrates excellent steady-state and dynamic performance, effectively reducing the torque and flux pulsations, computation load, and current harmonics. However, there are still several aspects [1] that need further research. (1) The weightless model predictive control strategy relies heavily on the prediction model parameters and sampling delay, which may lead to suboptimal experimental results. (2) The mathematical model of PMSM established in this study is based on simplifying assumptions, such as constant motor parameters, linear magnetic circuits, and neglecting eddy current losses, which may impact the control performance in actual applications, such as torque ripple, speed ripple, and current harmonics. Therefore, more accurate mathematical models should be considered in simulations, such as magnetic saturation effects, eddy current loss effects, and rotor damping effects. (3) In practical industrial applications of PMSM, various influencing factors, such as natural conditions (temperature, humidity, air pressure, etc. ), instrument precision (sensors, samplers, amplifiers, etc. ), and human factors (operational errors, improper maintenance, fault handling, etc.