**6. Conclusions**

In this study, a mechatronic inerter element was introduced into the structural design of vehicle seat suspensions, and the problem of optimizing the design of the vehicle seat suspension, to integrate the mechatronic inerter element, was investigated. In addition, the vertical and pitch movements of the vehicle's sprung mass and the vertical vibration of the seat were considered in a half vehicle model. Based on a ball-screw mechatronic inerter, the external electrical networks, using different transfer function-orders, were optimized via the particle swarm optimization algorithm. The results show that, as the external electrical network transfer function-order is increased, the RMS values of the seat acceleration and pitch acceleration will be further reduced. The RMS values of the seat acceleration and pitch acceleration can be simultaneously reduced by 10.56% and 7.57%, respectively, at most. The performance of vehicle seat suspensions with an integrated mechatronic inerter element can be improved by increasing the order of the external electrical network transfer function.

**Author Contributions:** Conceptualization, C.Q.; methodology, Y.S.; software, X.L.; validation, X.L.; formal analysis, C.Q.; investigation, Y.S.; writing—original draft preparation, C.Q.; writing—review and editing, Y.S.; supervision, X.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Natural Science Foundation of Beijing Municipality (No. 3214045), and the Natural Science Foundation of Jiangsu Province (No. BK20211364).

**Data Availability Statement:** The data used to support the findings of the study are available from the corresponding author upon request.

**Conflicts of Interest:** The authors declare no conflict of interest.
