## 4 Conclusions  
This study presented a performance optimization strategy for LPS used in SPV. The strategy mainly includes a multi-objective static performance optimization strategy and a dynamic performance experimental improvement strategy. By this optimization strategy, the optimized types of the LPS were manufactured and tested. The main conclusions are listed in the following:  
1. An equal yoke cross-sectional area simplified method was proposed in this study to reduce the time cost of the 3D FEA model of the LPS. The simplified 2D FEA model was verified by the comparison of the static push-force versus displacement curves. The simulation result and the measurement result indicated that the simplified 2D FEA model showed equal calculation accuracy with 3D FEA model and the time cost of the 2D FEA model was reduced more than 99.8% by comparison with 3D FEA model. 2. A multi-objective GA static performance optimization strategy was presented in this study to optimize the shape parameters of the LPS. An optimization fitness was proposed to obtain large push force and guarantee the deviation of the push force in the working stroke and improve the output efficiency (push force to mass ratio). The global optimization result was obtained and the manufactured. According to the comparison results of the manufactured optimal-type LPS and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Position** & **Conventional Type LPS** & **Optimal Type LPS** & **Electrical Steel Optimal Type LPS** \\ \hline start position & 31.6 Hz & 54.8 Hz & 72.4 Hz \\ middle position & 34.7 Hz & 52.8 Hz & 62.3 Hz \\ end position & 32.7 Hz & 51.5 Hz & 57.0 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cutoff frequency of the three types of the LPS at different position in the working stroke. Figure 17: The three types of manufactured LPSs. conventional-type LPS, the push force of the optimal-type LPS was increased by 21.8% in the rated current (total 1980 Ampere-turn magnetomotive force). Moreover, in low force requirement states, the optimal-type LPS also illustrated a good static performance. 3. A dynamic performance improvement strategy of increasing coil rated current was proposed. To certify the performance influence of the coil rated current, a theoretical analysis and an experimental test were employed. Both the theoretical results and test results could validate the advantage of increasing rated current. According to the comparison result of the manufactured optimal-type LPS and conventional-type LPS, the force response frequency of the optimal-type LPS were increased by 73.4%, 52.2% and 57.5%, respectively at start, middle and end position in the working stroke. 4. In addition, a dynamic performance improvement strategy of replacing magnetic material of the armature was proposed. To verify the influence of the magnetic materials, a theoretical analysis and an experimental test were also employed. Both the theoretical analysis and the experimental tests also validated the advantage of electric steel. According to the comparison results of the manufactured electrical steel optimal-type LPS and conventional-type LPS, the force response frequency of the electrical steel optimal type increased by 129.1%, 79.6% and 74.3%, respectively at start, middle and end position in the working stroke. From what have been discussed above, the improvement of the static optimization strategy and dynamic improvement strategy can be verified by the test results of the high accuracy device. However, some gaps also can be found in this study. For example, the deviation between simplified 2D FEA model and the measurement result can be reduced by considering the magnetic saturation phenomenon in the LPS. Moreover, an optimization algorithm and a multi-objective goal, which includes power loss and the current response time could be used to optimize coil winding parameters in further study. Conceptualization, S.W. ; methodology, S.W. ; software, S.W. ; validation, S.W. and Z.W. ; formal analysis, S.W. ; investigation, S.W. ; resources, Z.W.