## 1 Introduction  
Switched reluctance motors (SRMs) have gained increasing attraction in industry and academia because of their reliable structure, wide speed range, and high fault tolerance [1; 2]. However, the application of SRMs is limited by its inherent noise and torque ripple issues [3; 4]. These issues can be improved by optimizing the physical structure of the motor, but this approach does not apply to SRMs that have been produced or used. Therefore, many researchers are interested in solving the noise or torque ripple issue by using the advanced control strategy [5]. Many torque ripple optimization methods have been designed, and these methods can be roughly classified as indirect methods and direct methods. The indirect methods focus on splitting the total torque signal into phase reference signals using a torque sharing function (TSF) and keeping the total output torque constant by controlling the phase current. In [6; 7; 8], it is also proved that the phase torque can be controlled indirectly by adjusting the phase current. Since the phase reference signals are calculated from the sharing function, the control effect of this method is directly affected by the TSF [9]. In [10], the torque ripple suppression capabilities of linear, sinusoidal, cubic, and exponential TSFs are evaluated and improved, respectively. In conventional TSFs, due to their fixed parameters and limited voltage source, problems such as high current peak, high copper loss, and low-speed range may be generated [11; 12]. Therefore, many types of TSF are designed to accomplish the optimization of multiple control objectives simultaneously. In [13], in order to expand the applicable speed range of the TSF method, the commutation process is defined as two cases and a torque error proportional compensator is designed to reduce the maximum change rate of the flux linkage. In [14], an offline TSF is designed to optimize both torque ripple and copper loss. Since only one weight parameter is included in the objective function, the application of this method is simplified. In [15], an optimization problem is formulated based on the offline TSF, and the GA optimization algorithm is used to minimize the torque ripple and copper loss. In [16], an online optimization method for the TSF is developed to smooth the total output torque by compensating for the tracking error of the phase torque. Since the phase current is a direct control variable in the TSF method, it is also necessary to design an additional current controller. In [17], a PWM current controller with parameter adaption is proposed, which aims to improve the response speed and control accuracy of the phase current. In [18], in order to reduce the torque ripple, a predictive current controller is designed. Additionally, considering the disturbance in the system, an additional disturbance observer is proposed to improve the robustness of the current controller. In [19], a deadbeat predictive current controller is developed to achieve low torque ripple over the full speed range. The direct methods usually control the output state of the converter directly through the pre-established rule. Direct torque control (DTC) is a direct method to control flux linkage and torque simultaneously and was first applied to the SRM in [20]. In [21], the original six sectors in DTC are re-divided into nine and twelve sectors, and a new conduction rule is formulated to reduce the torque ripple. In [22], a new sector division method is developed to improve drive efficiency by avoiding the current extension into the negative torque region in the traditional DTC. The magnitude of flux linkage is required to be constant in the DTC, but this does not mean that the output torque is also constant, so it is pointed out in [23] that the closed loop of flux linkage should be removed. Direct instantaneous torque control (DITC) is another direct method with a simpler structure than DTC, which requires only hysteresis control of the torque [24].