## 1 Introduction  
Switched reluctance motors (SRMs) are gaining interest in various applications such as electric vehicle driving system, starter-generators system, and power supply for aerospace applications, because of the many advantages that the SRMs have in comparison to other motors, including their low cost, durability, simple structure and robust construction [1; 2]. Due to advances in high speed digital signal processing and power electronics technology, the controllable performance of the SRM has been improved greatly. However, one of the main drawbacks of the SRM used in servo-control is its large torque ripple, which leads to acoustic noise and vibration, thus causing the body vibration, transmission system parts damage, excessive bearings wear and even accidents involving the axis breaking [3; 4]. There are two main methods to reduce the torque ripple: one is to optimize the structure and magnetic design of the motor, and the other is to adopt the advanced control algorithm [5]. By optimizing the stator/rotor pole structures and the magnetic design, the torque ripple cannot be fully reduced, but the cost of the motor increases [6]. The main operating parameters of an SRM include the supply voltage, the turn-on and turn-off angles, the current level, and the shaft torque. And the control algorithm is based on selecting an optimum combination of these parameters [7; 8]. Therefore, an appropriate design for achieving a high SRM performance must take these factors into consideration and make an optimal choice. As an effective method for torque ripple reduction, direct instantaneous torque control (DITC) has gained interest in the last few years, due to its simple control structure, which provides greater flexibility for the torque ripple reduction [9; 10; 11; 12]. However, its implementation is not easy because it requires complex switching rules, uncontrolled switching frequency, and high sampling rates. In [9; 10], an iterative learning method for generating the optimized current waveforms was presented. In [11; 12], an online DITC technique that operates without torque profile functions and auxiliary phase commutating strategies was demonstrated. The optimal turn-on and turn-off angles for minimizing the torque ripple or the energy consumption has been described in [13; 14; 15]. In [16], a direct torque control based on the Lyapunov function was selected to minimize the torque ripples. In [17; 18], the machine design was combined with the control algorithms in an innovative method of profiling the phase currents to reduce the torque ripples of an SRM. In the latest research, the torque sharing function (TSF) has been investigated as an important and effective approach for minimizing the torque ripple in an SRM [19; 20; 21; 22; 23; 24]. Common TSFs curves contain linear, sinusoidal, exponential, cubic curves, and so on. In order to reduce the torque ripple, the phase current product and the individual phase torque harmoniously use the most suitable TSFs so that the total torque can align with the expected torque. Subsequently, the phase torque reference can be translated into the phase current reference based on the _T-i-\(\theta\)_ characteristics. With increasing speed of the SRM, the phase current cannot ideally follow its reference because of the limited phase voltage and therefore the torque ripples increase. In addition, because the phase current reference can be derived from the phase torque reference, the choice of the TSF directly affects the copper loss and the current tracking performance. The current tracking performance should be improved to enhance the torque-speed capability. Thus, in order to obtain an optimum TSF, it is necessary to consider a secondary objective that includes the maximization of the torque-speed range and the minimization of copper loss. These two evaluation criteria affect the torque-speed performance and the drive efficiency of the motor. In [19], four conventional common TSFs were studied and evaluated after optimization.