## 2 SRM Model  
The advantages of SRM's simple structure and high reliability can be attributed to the absence of magnets and windings on its rotor. A typical three-phase 12/8-pole SRM has 12 stator and 8 rotor poles, each phase contains four coil windings that can be excited simultaneously. The topology of the SRM and its asymmetric half-bridge converter is shown in Figure 1a. The anti-clockwise direction is the positive direction of the rotor angular position, and the aligned and unaligned positions of the rotor are defined as 22.5\({}^{\circ}\) and 45\({}^{\circ}\), respectively. When a phase is energized, the rotor tends to align with the energized stator poles and generates torque. In general, the phase torque can be expressed by the co-energy \(W_{c}\) as  
\[T_{p}(i_{p},\theta)=\left.\frac{dW_{c}(\theta,i_{p})}{d\theta}\right|_{i_{p}=const }=\frac{\partial\int_{0}^{i_{p}}\varphi_{p}(i_{p},\theta)di_{p}}{\partial \theta}\quad p=1,2,3 \tag{1}\]  
where \(p\) is the identifier of the phases. \(\theta,i_{p}\), and \(\varphi_{p}\) are the rotor angle, phase current, and phase flux linkage, respectively. The phase flux linkage \(\varphi_{p}\) can be represented by the phase inductance \(L_{p}\) and phase current \(i_{p}\) as  
\[\varphi_{p}(i_{p},\theta)=L_{p}(i_{p},\theta)\times i_{p} \tag{2}\]  
The highly nonlinear electromagnetic characteristics of the SRM make Equation (1) difficult to solve. The linear model shown in (3) can simplify the calculation effectively, but it is usually used for principle analysis because of the large difference from the actual model. Therefore, considering the model accuracy and computational complexity, the nonlinear model proposed in [4] is adopted and look-up tables (LUTs) are established to realize the proposed control strategy.  
\[T_{p}(i_{p},\theta)=0.5i_{p}^{2}\times\frac{dL_{p}(\theta)}{d\theta}=0.5i_{p}^ {2}L_{p}(\theta)^{\prime} \tag{3}\]  
The asymmetric half-bridge converter is very popular in the SRM drive system due to its high single-phase control flexibility and low hardware cost. Taking phase 1 as an example, three operating modes of 1, 0, and \(-1\) shown in Figure1b can be generated by  
Figure 1: SRM with excitation circuit and three switching states of the asymmetric bridge converter. (**a**) SRM with excitation circuit; (**b**) three switching states of the asymmetric bridge converter.  
turning on and off the two switches in each bridge arm. The red lines and arrows represent the path and direction of the current, respectively. In mode \(s=1\), the switches \(G_{1}\) and \(G_{2}\) are both turned on and the DC bus voltage \(V_{dc}\) is acted on the phase winding through the switches to make it excited. This mode can increase the phase output torque during torque generation. In mode \(s=0\), the switches \(G_{1}\) and \(G_{2}\) are turned on and off, respectively, and the phase winding is in the freewheeling mode through the switch \(G_{1}\) and diode \(D_{1}\). During torque generation, this mode can make the current decrease slowly, and the phase output torque can be reduced when the inductance rise rate is less than the square of the current decrease. In mode \(s=-1\), the switches \(G_{1}\) and \(G_{2}\) are turned off, and the phase winding is in the demagnetization mode. This mode can reduce the phase output torque by rapidly reducing the amplitude of the phase current during torque generation.  
In the asymmetric half-bridge converter, considering the voltage drop on the phase resistance and components, the phase voltages are expressed separately as  
\[\left\{\begin{array}{ll}V_{p,1}=V_{dc}-2V_{G}-V_{R}&s=1\\ V_{p,0}=-(V_{D}+V_{G}+V_{R})&s=0\\ V_{p,-1}=-(V_{dc}+2V_{D}+V_{R})&s=-1\end{array}\right. \tag{4}\]  
where \(V_{R}\) represents the phase winding voltage drop; \(V_{p}\) and \(V_{dc}\) are the phase voltage and DC voltage, respectively; \(V_{G}\) and \(V_{D}\) are the voltage drop across the semiconductor switch and diode, respectively. Since the values of \(V_{G}\) and \(V_{D}\) are very small, they are usually ignored to simplify the calculation.