**4. Discussion**

A 1/4 active suspension simulation model was established in MATLAB/Simulink, and a PSO-FNN-PID control algorithm was designed. By combining the PSO algorithm and the gradient descent method, the initial parameters of the FNN were optimized offline and then finetuned online, so as to obtain the optimal control rules and realize the real-time online adjustment of the PID control parameters. The combination of the two methods allowed the learning process to avoid falling into local minima while reaching the exact value at a later stage of learning. The simulation analysis indicated that the active suspension system with PSO-FNN-PID control had a preferable control effect compared with the passive suspension system and active suspension system with PID control, and could effectively attenuate the body vibration caused by external disturbance. Therefore, an examination of the graphs and data reveals that the PSO-optimized FNN-PID controller has significantly superior performance, and is capable of enhancing the vehicle's road adhesion and ensuring a smooth and comfortable ride. In the future, we will continue to explore the possibility of implementing this control system in the whole vehicle system and consider the development and implementation of related hardware and software. In addition, we also hope to make some changes to the basic PID control, such as including an integral anti-saturation control strategy, in order to obtain better results.

**Author Contributions:** Conceptualization, M.L. and J.L.; methodology, M.L.; software, J.L.; validation, J.L. and J.X.; formal analysis, J.L.; investigation, G.L.; resources, M.L.; data curation, J.L.; writing—original draft preparation, G.L.; writing—review and editing, M.L.; visualization, J.X.; supervision, M.L.; funding acquisition, M.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Natural Science Foundation of Hainan Province, gran<sup>t</sup> number 2019RC144, and supported by China Scholarship Council, gran<sup>t</sup> number 202007565009.

**Data Availability Statement:** Not applicable.

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