###### Abstract  
The permanent-magnet synchronous motor (PMSM), with the advantages of low energy consumption and stable operation, is considered a green power source to replace gasoline engines. Motor control is the core problem of the electric-drive system, so it is important to study the high-performance motor control algorithm. The traditional PMSM control strategy has problems such as torque pulsation, large overshoot, and parameters which are not easy to adjust. This work proposes a new model-predictive torque control (MPTC) based on multi-objective ranking for these issues. The Romberg observer was utilized to accurately estimate motor flux and torque across a wide range of speeds and ensure optimal performance of the MPTC. The optional voltage vectors were classified using graph theory. The model's cost function was optimized and the control delay caused by hardware processing was compensated by a modified Euler method. A multi-objective ranking method was used to avoid the offline selection of MPTC weight coefficients. Additionally, one ranking method was used to reduce the complexity of the algorithm for multiple objectives. Based on the simulation results, the newly proposed MPTC method, when compared with traditional approaches, reduced the total harmonic distortion from 2.78% to 2.26%. Torque ripple decreased by approximately 58.4%, and the switching frequency was reduced by 3.05%, lowering the inverter's switching losses. Therefore, the newly proposed MPTC had faster torque response, reduced computation time, and less torque pulsation, which further improved the dynamic performance of the permanent-magnet synchronous motor. permanent-magnet synchronous motor; model-predictive control; multi-objective sorting; model-predictive torque control Article  
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are calculated and compared with the predetermined torque and flux values. The resulting differences are utilized for direct control of flux and torque [4]. Hence, DTC features a simple control structure and excellent dynamic performance. However, DTC produces variable switching frequencies with large fluxes and torque ripple, which result in high-frequency noise. Researchers have studied some strategies, e.g., employing space vector modulation (SVM) to control voltage inverters [5] or introducing duty-cycle control [6] and DTC based on sliding mode speed controller [7] to solve these problems. Due to the characteristics of permanent-magnet synchronous motors (PMSM), such as nonlinearity, strong coupling, and numerous variable parameters, traditional vector control methods like Field-Oriented Control (FOC) and Direct Torque Control (DTC) often fall short of meeting the demands of high-performance, high-precision, and robust operation [8]. To enhance the control performance of PMSMs, numerous researchers have proposed advanced control strategies, including intelligent control [9], sliding mode control [10], and predictive control [11]. Intelligent control methods encompass neural networks and fuzzy control, among others. The essence of intelligent control lies in autonomy, mimicking human thought processes to achieve intelligent control. For instance, [PERSON] et al. [12] achieved precise observation of electromagnetic torque using a BP neural network. [PERSON] and others [13] proposed a continuously adaptive RBF network for speed control of interior permanent-magnet synchronous motors, simplifying the control structure while enhancing control accuracy. However, intelligent algorithms such as neural networks and machine learning typically require extensive training data, exhibiting limited robustness and flexibility in PMSM systems [14]. When dealing with multiple objectives, some intelligent algorithms necessitate retraining, adding to the workload. Moreover, the significantly increased computational complexity due to intelligent algorithms hampers the motor's ability to respond rapidly [15].