## 1 Introduction
Conversely, in [19], a partial prefilter in which the prefilter is solely used for the resonant controller is designed, while a traditional PI controller is used for constant disturbance mitigation. However, the arrangement of the partial prefilter poses considerable difficulties. An alternative approach for the observation of disturbances involves the application of disturbance observers (DOBs), which enable the seamless achievement of TDOF control [20]. The primary objective of DOBs is to estimate disturbances by compelling the predicted output to align with the actual output of the system. Likewise, controllers employed in feedback regulation can be applied within observers. For instance, a proportional regulator may be integrated into a DOB, while a PI regulator could be utilized in an ESO. Research indicates that various DOBs act as low-pass filters in perturbation detection [21]. Thus, general PI observers [22] may be inadequate for periodic tracking. Similarly, quasi-fractional-resonant normalized extended state observers (NESOs) have been introduced to suppress speed ripple caused by current measurement errors [23]. These methods highlight the potential of advanced observer designs in mitigating periodic disturbances and ensuring robust control. In [24], in order to mitigate the sixth-order current harmonics resulting from the dead time effect in resonant controllers, the DOB is applied, allegedly using a dual-loop configuration. Nonetheless, the experiments are restricted to a low-speed regime, with the maximum resonant frequency capped at 60 Hz. A thorough design methodology for this particular type of DOB, along with a corresponding stability analysis, is presented in [25]. In contrast to the DOB-centric control methodology, the ADRC utilizing an ESO exhibits enhanced efficacy in mitigating measurement noise due to its ability to simultaneously observe both speed and disturbances. In [26], a GIESO is used to minimize the current harmonics induced by an imbalanced grid. This leads to a higher maximum resonance frequency of 300 Hz. However, the analysis does not consider higher frequency disturbances. It also overlooks the effects of the one-step delay induced by PWM updates. In order to improve the robustness of the system to frequency deviations, a quasi-resonant ESO is introduced in [27]. The controller is formulated in the discrete time domain, which facilitates dealing with one-step delays. Analysis shows that if the sampling interval is too large, the system may become unstable. However, high frequency disturbances are also ignored. In [28], PIR is used as current control to counteract the higher-order harmonics of the torque ripple. This eliminates the delay associated with the inner current loop. On the other hand, implementing a PIR current controller increases the complexity of the algorithm. Reflecting on the earlier analyses, this paper unveils an innovative integrated torque harmonic extended state observer (ITHESO) incorporated within a decoupled current control schema, specifically intended to diminish torque ripple in the VFRM. The proposed ITHESO, unlike ADRC and GIESO, integrates the torque harmonic component to effectively reduce torque ripple while also addressing the inter-axis couplings present in the current loop control, thereby bypassing the complexities faced with the PIR controller. Initially, a comprehensive assessment of the current control loop is undertaken to validate that VFRMs are characterized by intricate inter-axis couplings and torque ripple. To address this challenge, the ITHESO is formulated. In this approach, the torque harmonic is treated as a periodic disturbance and integrated into each of the dq0-axis current controllers, while the validation of the system's stability is ensured through the application of principles outlined by [PERSON]'s stability theory. Experimental evaluations substantiate the efficacy of the proposed decoupled current control strategy.