## 1 Introduction
However, repetitive control requires high accuracy of the center frequency, necessitating the integration of frequency adaptation algorithms in practical applications where the center frequency may vary. The current harmonic suppression algorithm, based on the Extended State Observer (ESO), treats current harmonics as disturbances and eliminates them through the state observer. Due to the low model precision requirements of ESO, the algorithm demonstrates strong robustness against parameter variations and external disturbances. In [13], the authors designed an Extended Harmonic State Observer (EMSO) to estimate and suppress multiple harmonic disturbances. In [14], the authors addressed three shortcomings of traditional ESO by proposing three enhanced ESOs to tackle the current harmonic issues in permanent magnet motors. However, improper gain settings in ESO can introduce stability problems, particularly oscillations under high gain settings. Sliding Mode Control (SMC) has garnered significant attention from researchers in the field of harmonic suppression in motor drives due to its robustness against system parameter variations and external disturbances. However, traditional SMC strategies often face the challenge of chattering, which limits their practical applications. This issue has been addressed by integrating advanced control techniques and algorithms. In one set of studies, improved control strategies were employed to optimize the performance of SMC. For instance, the Speed-Adaptive Super-Twisting Control (S-AST) proposed in [15], which combines Proportional-Integral (PI) and Super-Twisting (ST) controllers, significantly reduces chattering and effectively lowers the total harmonic distortion (THD) in PMSMs. Additionally, the current harmonic and imbalance suppression strategy based on vector space decomposition control, as discussed in [16], successfully mitigates the fifth and seventh current harmonics and addresses imbalance issues. In another set of studies, advanced control technologies were used to enhance harmonic suppression. In [17], the authors employed a continuous fractional-order sliding mode control strategy based on the Output Feedback Feature Selection Neural Network (OFFSETNN), significantly improving power quality and harmonic suppression in the grid. These advancements demonstrate the potential of integrating innovative control techniques to overcome traditional challenges in SMC, thereby broadening its application in motor drive systems. Another strategy for harmonic suppression is the use of resonant controllers, which offer high computational efficiency and flexibility. Compared to ideal resonant controllers, quasi-proportional-resonant controllers increase the bandwidth of the resonant frequency, thereby enhancing system stability. Additionally, by integrating the benefits of proportional control, these controllers improve the response across the entire frequency range. As a result, quasi-proportional-resonant controllers effectively compensate for harmonic currents, reducing their content and achieving harmonic current suppression. This makes them a more suitable choice for complex and demanding practical applications [18]. Resonant controllers have been extensively studied for their excellent performance in precise harmonic suppression. In one line of research focused on optimizing resonant controllers, a Small Phase Angle Resonant Controller (SPARC) was proposed in [19]. This controller addresses the excessive phase angle issue at the resonant frequency found in traditional resonant controllers, significantly enhancing the suppression of current harmonics in PMSM. In another line of research, composite resonant control strategies that combine other control techniques have been explored. For instance, in [20], the authors proposed a low-order current harmonic suppression strategy based on a Butterworth filter and a quasi-proportional-resonant controller, optimizing current harmonic suppression in traction drive systems.