# An NUTSF at Sub-Region for Suppression of Torque Ripple in Switched Reluctance Motors
## 4 Proposed NUTSF Control Strategy
### Principle of the Proposed Control Strategy  
It is shown how the NUTSF works in Figure 7 where the \(T_{ref}(k-1)\) and \(T_{ref}(k)\) are the torque reference of the outgoing phase and incoming phase, respectively. Figure 6: Region allocated diagram of NUTSF control based on inductance characteristics. Figure 7: Torque reference of NUTSF. As for the incoming phase in region 1, the torque reference of the incoming phase is required to rise gently by using \(q_{up1}(\theta)\) in order to make the actual torque of the incoming phase track the torque reference \(T_{ref}(k)\); therefore, the torque reference of the incoming phase conforms more to the rising trend of the actual torque of the incoming phase. A large change rate of inductance of the outgoing phase can produce a larger torque in region 1, while a small change rate of inductance of the incoming phase can produce a smaller torque. Thus, in region 1, the torque required for SRM operation is mainly provided by the outgoing phase. The increased torque of the incoming phase should be equal to the decreased torque of the outgoing phase in order to keep the total torque constant, so the torque reference of the outgoing phase \(T_{ref}(k-1)\) is gently adjusted downward by using \(q_{down1}(\theta)\). In region 2, the change rate of the inductance of the incoming phase becomes larger, and the current continues to increase, so the torque of the incoming phase becomes larger. The torque required for SRM operation is mainly provided by the incoming phase. Thus, the torque reference of the incoming phase should rise rapidly, and the torque reference of the outgoing phase should be decreased rapidly so that the total torque is kept constant and negative torque of the outgoing phase is not produced. Therefore, the torque reference \(T_{ref}(k-1)\) of the outgoing phase in region 2 is adjusted by \(q_{down2}(\theta)\) to decrease rapidly, while the torque reference \(T_{ref}(k)\) of the incoming phase is adjusted by \(q_{up2}(\theta)\) to increase rapidly. In this way, the SRM produces a stable total torque and reduces the torque ripple. The NUTSF control strategy is proposed to change the shape of the TSF, which makes the shape of torque reference more in line with the changing trend of actual torque. The comparison between the NUTSF and the conventional TSF is shown in Figure 8 where the solid line indicates the NUTSF and the dotted line indicates the conventional TSF. The slope of the NUTSF of the incoming phase and the outgoing phase in region 1 is small, while the slope in region 2 is steeper, and the torque reference of the incoming phase and the outgoing phase in region 1 and region 2 is better fitted to the change rate of inductance and the actual torque of each phase. The slope of the function in each region is determined by the \(P1\) th-power and \(P2\) th-power of the TSF. The th-power of \(P1\) and \(P2\) are determined by the optimization algorithm of the TSF. Whether the th-power of \(P1\) and \(P2\) is changed depends on whether the torque error is within the specified range. The shape of the TSF is adjusted further; therefore, torque ripple will reduce further. The control flow chart is shown in Figure 9. Firstly, the initial values \(P1_{(0)}\) and \(P2_{(0)}\) are input, and then the torque error formula is used to obtain the torque error values \(\Delta T_{1}\) and \(\Delta T_{2}\) in regions 1 and 2, and the torque error formula is obtained from Formula (8)  
\[\left\{ \begin{array}{l}\Delta T_{1}=\Delta T_{a}+\Delta T_{b}=\left[T_{ref}(k -1)-T(k-1)\right]+\left[T_{ref}(k)-T(k)\right]\\ \Delta T_{2}=\Delta T_{c}+\Delta T_{d}=\left[T_{ref}(k-1)-T(k-1)\right]+\left[ T_{ref}(k)-T(k)\right]\end{array} \right. \tag{8}\]  
where \(\Delta T_{1}\) and \(\Delta T_{2}\) are the total torque errors in region 1 and region 2, respectively; \(\Delta T_{a}\) and \(\Delta T_{d}\) are the torque errors of the outgoing phase in region 1 and region 2, respectively; \(\Delta T_{b}\)  
Figure 8: Comparison between conventional TSF and proposed NUTSF.