# Predictive Current Control for Switched Reluctance Motor Based on Local Linear Phase Voltage Model
## 2 Predictive Current Control
### Average Voltage Regulation  
In this paper, the phase current is controlled by regulating the average phase voltage with PWM. The PWM generation mechanism for positive and negative average voltage is shown in Figure 2, where \(DM_{1}\) and \(DM_{2}\) are PWM drive signals for M\({}_{1}\) and M\({}_{2}\), respectively; \(CR_{1}\) and \(CR_{2}\) are the comparison values for \(DM_{1}\) and \(DM_{2}\), respectively; \(CTR\), \(M_{\rm CTR}\) and \(T_{\rm P}\) denote PWM counter, maximum value of the counter and PWM cycle, respectively; \(E_{1}\) indicates an event where the larger comparison value matches the down-counting PWM counter, and \(E_{2}\) indicates an event where the larger comparison value matches the up-counting PWM counter. The PWM signals are conventionally generated in center-aligned mode, where the PWM signals are symmetrical with respect to the point where counter underflows. The duty cycle depends on the amplitude relationship between the PWM counter and the corresponding comparison value. A positive average voltage is generated by applying positive DC-link voltage and zero voltage at different times of a PWM cycle, while a negative average voltage is generated by applying negative DC-link voltage and zero voltage at different times. An average voltage ranging from \(-U_{\rm dc}\) to \(U_{\rm dc}\) can also be directly implemented by applying positive and negative DC-link voltage at different times of a PWM cycle. However, the current ripple and switching losses will be larger. The update instant of the comparison values is considered. It is recommended to update the comparison values right at the overflow of the PWM counter. Thus, positive and negative average voltage in a PWM cycle can be simply calculated by Equations (6) and (7), respectively. Otherwise, the average voltage calculation could be much more complicated  
Figure 2: PWM generation mechanism. (**a**) Positive average voltage. (**b**) Negative average voltage. \(\overline{v}_{\text{A},k,k+4}\) should also satisfy Equation (11). \[ \begin{array}{ll}\overline{v}_{\text{A},k,k+4}\bigtriangleup t_{\text{A},k,k+4}& =\overline{v}_{\text{A},k,k+1}\bigtriangleup t_{\text{A},k,k+1}+\overline{v}_ {\text{A},k+1,k+4}T_{\text{P}}\\ &=\overline{v}_{\text{A},k+1,k+4}T_{\text{P}}\end{array}  \tag{11}\]  
where \(\overline{v}_{\text{A},k+1,k+4}\) is the average voltage required in the next PWM cycle. Combining Equations (8)-(11), \(\overline{v}_{\text{A},k+1,k+4}\) can be predicted by  
\[ \begin{array}{ll}\overline{v}_{\text{A},k+1,k+4}=f_{\text{P}}\bigtriangleup t _{\text{A},k,k+4}\overline{v}_{\text{A},k-1,k}+\\ \frac{f_{\text{P}}\bigtriangleup t_{\text{A},k-3,k-1}(\overline{v}_{\text{A },k-3,k-1}-\overline{v}_{\text{A},k-1})\big{(}\bigtriangleup t_{\text{A},k+4} \bigtriangleup t_{\text{A},k-1}-\bigtriangleup t_{\text{A},k-1}\bigtriangleup t _{\text{A},k+4}\bigtriangleup t_{\text{A},k+4}\bigtriangleup t_{\text{A},k-3, k-1}\bigtriangleup t_{\text{A},k-1}\bigtriangleup t_{\text{A},k+4}\bigtriangleup t _{\text{A},k-3,k-1}}\end{array}  \tag{12}\]  
where \(f_{\text{P}}\) is the PWM frequency. As can be seen from Figure 3, \(\overline{v}_{\text{A},k-3,k-1}\) is fixed to zero. Thus, Equation (12) can be simplified to Equation (13). \[ \begin{array}{ll}\overline{v}_{\text{A},k+1,k+4}=f_{\text{P}}\overline{v}_ {\text{A},k-1,k}\bigtriangleup t_{\text{A},k,k+4}-\\ \frac{f_{\text{P}}\overline{v}_{\text{A},k-1,k}\bigtriangleup t_{\text{A},k-3, k-1}\big{(}\bigtriangleup t_{\text{A},k,k+4}\bigtriangleup t_{\text{A},k-1} -\bigtriangleup t_{\text{A},k-1}\bigtriangleup t_{\text{A},k+4}\bigtriangleup t _{\text{A},k-3,k-1}\bigtriangleup t_{\text{A},k-3,k-1}\bigtriangleup t_{ \text{A},k-3,k-1}}\end{array}  \tag{13}\]  
According to Figures 2 and 3, \(\Delta t_{\text{A},k-3,k-1}\), \(\Delta t_{\text{A},k-1,k}\) and \(\Delta t_{\text{A},k,k+4}\) can be obtained as Equations (14)-(16), respectively. \[\begin{array}{ll}\bigtriangleup t_{\text{Awhere \(T_{\rm cal}\) denotes the calculation time.