## 5 Conclusions  
In this paper, LQSOFCs and PACs were designed and applied to reduce the heave acceleration and the pitch rate of the sprung mass for RC enhancement and MS reduction. HCM was chosen as a vehicle model, and the SSEQN was derived from it. With the SSEQN and LQOF, LQR is designed. To avoid the full-state feedback of LQR which is very difficult to implement in a real vehicle, two types of SOF structure were proposed and optimized with the LQOF by the meta-heuristic method, CMA-ES. PACs were designed with the two SOF structures which are set to make the suspension forces be zero. The PACs updated adaptively the gains of SOF controllers with the extended Kalman filter in every time step. To validate the proposed method regarding RC and MS, the simulation was performed on CarSim. Based on the simulation responses, it was identified that the proposed PACs are quite effective in enhancing RC and reducing MS. It was also shown that PACs are effective on three road profiles. From simulation responses, the concluding points were identified as follows:  
1. PACs outperform LQSOFCs on three road profiles. PACs show very good performance below 5 Hz with respect to RC and MS, which is the actuator bandwidth. On the other hand, PAC2 is slightly better than PAC1 because the former uses four signals for control and the latter does two signals. For those reasons, PAC2 is recommended due to its simpler structure and smaller number of sensor signals. 2. LQSOF1 shows worse performance than LQSOF2 on LHSB and SWR. This results from the suspension displacements and suspension velocities in CarSim are smaller than those in the linear SSEQN. On the contrary, LQSOF2 show better performance because it uses only the vertical velocity and pitch rate of SPMS. Instead, LQSOF2 shows worse performance than the uncontrolled case within the range from 5 to 9 Hz. In a comprehensive way, LQSOFCs are not recommended for ride comfort enhancement and motion sickness mitigation. In further research, the performance of the proposed PAC will be verified by experiments on small-scale devices, on hardware-in-the-loop (HIL) environments or on a quarter-car test rig. The procedure to obtain suspension velocities and suspension displacements with accelerometers, as given in Figure 3, can be easily implemented in real vehicles. If a relevant actuator is selected, the proposed method in this paper can be implemented on real vehicles and tested on various scenarios. In addition to the implementation issues, based on the SOF structures proposed in this paper, neural networks or reinforcement learning will be applied for RC enhancement and MS reduction. This is a natural consequence due to the fact that RLS, EKF, neural networks and reinforcement learning are learning-based algorithms. Conceptualization, S.Y. ; methodology, S.Y. ; software, J.K. and S.Y. ; validation, J.K. and S.Y. ; formal analysis, S.Y. ; investigation, J.K. and S.Y. ; resources, S.Y. ; data curation, J.K. and S.Y. ; writing--original draft preparation, J.K. and S.Y. ; writing--review and editing, J.K.; visualization, J.K.; supervision, S.Y. ; funding acquisition, S.Y. All authors have read and agreed to the published version of the manuscript. This work was supported by the Ministry of Education through the National Research Foundation of Korea (NRF) under Basic Science Research Program (RS-2019-NR040071). Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author/s. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: