# 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
and \(\Delta T_{c}\) are the torque errors of the incoming phase in region 1 and region 2, respectively; \(T_{ref}(k-1)\) is the torque reference of the outgoing phase, \(T(k-1)\) is the torque of the outgoing phase, \(T_{ref}(k)\) is the torque reference of the incoming phase, \(T(k)\) is the torque of the incoming phase. It can be seen from Formulas (5), (7) and (8) that \(T_{ref}(k-1)\) and \(T_{ref}(k)\) in \(\Delta T_{1}\) and \(\Delta T_{2}\) are related to the torque sharing function. Formula (7) shows that the th-powers \(P1\) and \(P2\) affect the torque sharing function, which means that the torque errors \(\Delta T_{1}\) and \(\Delta T_{2}\) will be affected by \(P1\) and \(P2\). Therefore, it is useful to set \(P1\) and \(P2\) properly to reduce torque errors \(\Delta T_{1}\) and \(\Delta T_{2}\) at different speeds, improve the torque tracking ability and reducing torque ripple. The adjustment formula of \(P1\) and \(P2\) is shown in Formula (9). \[\left\{ \begin{array}{l}P1=P1_{(n)}=P1_{(0)}\pm\Delta P\\ P2=P2_{(n)}=P2_{(0)}\pm\Delta P\end{array} \right. \tag{9}\]  
where \(P1_{(n)}\) and \(P2_{(n)}\) are the new th-power of \(P1\) and \(P2\), respectively, in the iteration, and \(\Delta P\) is the increment of the \(P1\) th-power and \(P2\) th-power value. Whether \(P1_{(0)}\) and \(P2_{(0)}\) in region 1 and region 2 increase \(\Delta P\) or decrease \(\Delta P\) depends on whether \(\Delta T_{1}\) and \(\Delta T_{2}\) are positive or negative. If \(\Delta T_{1}\) is positive in region 1, the present torque references \(T_{ref}(k-1)\) and \(T_{ref}(k)\) are large. It is concluded from Formulas (7)-(9) that the value of \(P1\) needs to be increased in this case in order to slow down the shape of the NUTSF, therefore reducing the value of the torque reference. If \(\Delta T_{1}\) is negative, the torque references \(T_{ref}(k-1)\) and \(T_{ref}(k)\) are small. It is necessary to reduce the value of \(P1\)  
Figure 9: Optimization algorithm of torque sharing function. so that the shape of the NUTSF is intensified, increasing the torque reference. Similarly, the \(P2\) in region 2 can be obtained. The torque errors of \(\Delta T_{1}\) and \(\Delta T_{2}\) in each region should be adjusted according to error limit \(v\), which is set based on the desired rate of torque ripple \(\gamma\). The limit formula is shown as Formula (10). \[v=\frac{1}{2}T_{ref}\gamma \tag{10}\]  
where \(v\) is the error limit, and \(\gamma\) is the desired rate of torque ripple. If the torque errors \(\Delta T_{1}\) and \(\Delta T_{2}\) in region 1 and 2 are within the torque error limit, the present \(P1_{(n)}\) and \(P2_{(n)}\) are taken as the output of the controller, and the latest values of \(P1\) th-power and \(P2\) are obtained; that is, \(P1=P1_{(n)}\) and \(P2=P2_{(n)}\). If \(\Delta T_{1}\) and \(\Delta T_{2}\) are not within the error limit, the values of \(P1\) and \(P2\) will be changed iteratively until the condition is satisfied. According to the above-mentioned TSF optimization algorithm, the overall control system block diagram of the NUTSF control strategy is shown in Figure 10. The algorithm adjusts the TSF in region 1 and 2 online, and distributes the total torque reference by the new TSF module, which improves the torque tracking ability in the TpE and reduces the torque ripple at different speeds.