## 1 Introduction  
PMSMs are renowned for their high efficiency, rapid response, and low power losses, making them widely used in high-precision AC servo systems and electric vehicle drives [1]. However, distortions in the motor air gap magnetic field, along with non-ideal factors such as inverter dead-time effects and voltage drop across devices, introduce harmonic components into the stator current. These harmonic components, specifically the 5 th, 7 th, 11 th, and 13 th harmonics, contribute to periodic torque ripples [2]. Among these, the fifth and seventh harmonics are particularly detrimental to speed control systems. The interaction between the fifth and seventh harmonics in the stator current and the fundamental magnetic field of the rotor's permanent magnets generates a sixth-order torque ripple. These ripples cause fluctuations in motor speed, thereby reducing the precision of servo control systems. Consequently, the primary focus of harmonic control in PMSMs is on mitigating the fifth and seventh harmonics. Extensive research has been conducted both domestically and internationally on suppressing harmonic currents, improving motor current waveforms, and mitigating torque ripples [3]. These methods can be categorized into two main approaches. The first approach focuses on motor design, primarily optimizing the motor structure to enhance the sinusoidal distribution of the air-gap magnetic field [4]. However, this complicates the motor structure and increases manufacturing costs. The second approach emphasizes system control strategies, employing harmonic compensation algorithms to suppress current harmonics. This method has the advantages of not requiring additional hardware and being easily integrated into motor systems. Therefore, this paper focuses on the use of control algorithms to suppress current harmonics. The advantages of Iterative Learning Control (ILC) lie in its high control precision and independence from the mathematical model of the control system, making it widely used in reducing current harmonics and torque fluctuations [5; 6]. Existing research leverages ILC to optimize motor performance by dynamically adjusting control strategies to minimize harmonic errors and disturbances. In [7], the authors proposed a rotor position harmonic error suppression method based on adaptive ILC for sensorless PMSM drives that does not require offline detection and identification of harmonic frequencies and exhibits strong suppression capabilities for various harmonic error components. Furthermore, In [8], the authors introduced a torque ripple suppression method for PMSM based on SMA-optimized ILC, which does not rely on prior knowledge of system and motor parameters and reduces torque ripple by mitigating the effects of higher-order harmonics in the control current. However, its complex structure and significant computational burden pose considerable challenges for practical applications. Current harmonic suppression technology based on repetitive control methods offers high steady-state accuracy, minimal parameter adjustments, and simple control structures [9]. Various studies have focused on different aspects and improvements of repetitive control technology. In one group of studies, the structure and system integration of repetitive controllers were optimized. In [10], the authors constructed three closed-loop systems using a power amplifier and repetitive controller, achieving high-precision suppression of harmonic vibration forces. Another group of studies focuses on the algorithmic optimization of repetitive control. In [11], the authors explored a hybrid control method combining second-order odd harmonic repetitive control and finite-dimensional repetitive control, effectively addressing the non-integer delay problem in digital repetitive control. Additionally, in [12], the authors proposed an adaptive odd-order repetitive control method capable of suppressing odd harmonic currents in magnetic suspension bearings without the need for a speed sensor.