# A Novel Adaptive PID Controller with Application to Vibration Control of a Semi-Active Vehicle
## 5 Conclusions  
In this work, a new adaptive hybrid controller based on the H-infinity control technique, sliding mode controller and PID controller was formulated and applied to vibration control of an MR seat suspension system to demonstrate its effectiveness. In the formulation of the hybrid controller, the online interval type 2 fuzzy and the Riccati-like equation were also used for combining three controllers. The parameters of the Riccati-like equation were determined to follow the change of system based on the fuzzy model and sliding surface of the sliding mode controller. The stability of the proposed hybrid adaptive controller was then solidly proven by adopting Lyapunov stability criterion. Subsequently, the proposed controller was applied to vibration control of MR seat suspension system of commercial vehicles such as bus and truck. Control performances were evaluated through both computer simulations and experimental realization by integrating the microprocessor. In order to validate robust stability of the proposed control system, three different road profiles were adopted and used for the excitations; random bump excitation, regular bump excitation, and random-step-wave excitation. After showing the effectiveness and characteristics of the proposed controller using computer simulations, experimental tests were undertaken to achieve control results for the excited vibrations. It has been shown from experimental realization that the proposed controller can reduce unwanted vibrations at the seat and the driver position satisfying the regulation of the ISO 2631-1. The results presented in this work are quite self-explanatory, justifying that an appropriate hybrid controller which consists of several classical/modern controllers and intelligent controllers can significantly improve the effectiveness of control performances much better than the implementation of a single controller. Notably, the control effectiveness of the hybrid controller is highlighted for complicated systems subjected to parameter variations and external disturbances. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{3}{c}{**Bump Regular Excitation**} \\ \cline{2-4}  & **Proposed Control** & **Control [5]** & **Control [17]** \\ \hline ToD & 0.262262 & 0.289031 & 0.274320 \\ ToA & 0.579926 & 0.699909 & 0.583241 \\ \hline \multirow{2}{*}{**Index**} & \multicolumn{3}{c}{**Random Step Wave Excitation**} \\ \cline{2-4}  & **Proposed control** & **Control [5]** & **Control [17]** \\ \hline ToD & 0.349026 & 0.586984 & 0.398267 \\ ToA & 0.585122 & 0.732741 & 0.608735 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Evaluation values of ToD and ToA. **Acknowledgments:** This work was supported by 2017 Inha University Research Grant. This financial support is gratefully acknowledged. **Author Contributions:** [PERSON] conceived and designed the experiments; [PERSON] and [PERSON] performed the experiments; [PERSON] and [PERSON] analyzed the data and wrote the paper. **Conflicts of Interest:** The authors declare that there is no conflict of interest.