4.2. Control results of the HAC-IFV

In simulation of the HAC-IFV, the values of the sliding surface [k1, k2] are chosen by [1, 1.10�<sup>5</sup> ]. The constant value Γ of the Riccati-like equation is chosen by 40, 10 for the regular bump road, the random step wave road, respectively. The constants α1, α<sup>2</sup> of adaptation laws are chosen as 10 for all road profiles. The values of εf, ε<sup>g</sup> of the expanded adaptation laws are chosen by 10 and the values of δ1, δ<sup>2</sup> are chosen by 0.05. In this simulation, the initial states for the dynamic states are used as 0½ � :122 2:5 , 0½ � :066 2:5 , 0½ � :047 2:5 for random bump, random regular bump, and random step wave bump, respectively. The initial states for the observer are ½ � 0:06 0 for two excitations. It is noted that the observer is applied to evaluate the results of the proposed controller. The parameters [k1, k2] are chosen as [1, 1.5] for random regular bump and [1, 5] for random step wave bump.

Robust Adaptive Controls of a Vehicle Seat Suspension System http://dx.doi.org/10.5772/intechopen.71422 19

Figure 8. Control results with the HAC-IFV at the seat (xs): (a1, a2) random step wave road, (b1, b2) regular bump road.

performance. These results mean that the application of the prescribed performance in design of the hybrid adaptive controller can improve the quality of control with high robustness

Figure 7. Tracking error with the HAC-PP: (a1, a2) random step wave road, (b1, b2) regular bump road.

In simulation of the HAC-IFV, the values of the sliding surface [k1, k2] are chosen by [1, 1.10�<sup>5</sup>

The constant value Γ of the Riccati-like equation is chosen by 40, 10 for the regular bump road, the random step wave road, respectively. The constants α1, α<sup>2</sup> of adaptation laws are chosen as 10 for all road profiles. The values of εf, ε<sup>g</sup> of the expanded adaptation laws are chosen by 10 and the values of δ1, δ<sup>2</sup> are chosen by 0.05. In this simulation, the initial states for the dynamic states are used as 0½ � :122 2:5 , 0½ � :066 2:5 , 0½ � :047 2:5 for random bump, random regular bump, and random step wave bump, respectively. The initial states for the observer are ½ � 0:06 0 for two excitations. It is noted that the observer is applied to evaluate the results of the proposed controller. The parameters [k1, k2] are chosen as [1, 1.5] for random regular bump

].

against severe excitations.

18 Adaptive Robust Control Systems

4.2. Control results of the HAC-IFV

and [1, 5] for random step wave bump.

Figures 8–10 present control responses of the HAC-IFV. As similar to the HAC-PP, the initial excitations were remarkably reduced by applying the proposed controller. The displacements at the seat and driver positions are reduced resulting in the improvement of the ride comfort. In order to demonstrate a salient benefit of the proposed controller, its control response is compared obtained from the controller proposed in [17, 25]. It is clearly identified that the convergence time of the displacement of the proposed controller is 2 seconds for both excitations, while that is 15 seconds for the random step wave excitation, 6 seconds for regular bump excitation in [17, 25]. In Figure 8, the sliding surfaces of three controllers are shown. It is observed that the proposed control obtains stable motion much faster than the comparative controls at 0.1 second. It is noted here that the better control responses of the proposed controller comes from the inversely fuzzified values in given Eqs. (46)–(48). In Eq. (48), the independent of the inversely fuzzified value helps the controller to increase its robustness. This new exploration is the outstanding property of the proposed controller in the severe operation environment subjected to strong and random disturbances.

5. Concluding remarks

Acknowledgements

acknowledged.

Author details

University, Incheon, Korea

Do Xuan Phu1

mances to appropriately select each control scheme.

Declaration of conflicting interest

The authors declare that there is no conflict of interest.

\*Address all correspondence to: seungbok@inha.ac.kr

Vietnamese-German University, Binh Duong, Vietnam

, Ta Duc Huy1 and Seung Bok Choi<sup>2</sup>

In this study, two new adaptive controllers were formulated and their effectiveness was validated by applying them to vibration control of a semi-active vehicle seat suspension system featuring MR damper. The first adaptive controller includes two sliding mode controls: one for initial states of the system and the other for prescribed performance associated with the parameters of the modified Riccati-like equation. By doing this way, the tracking performance is enhanced resulting in the improved control responses. The second adaptive controller was formulated on the basis of the inversely fuzzified value with the H-infinity control to minimize computational cost algorithm. Hence, by doing this way, the convergence time can be reduced resulting in high stability of the system subjected to severe external disturbances. It has been sown that the proposed two adaptive controllers can significantly reduce the excitation from the road profiles at both the seat and driver positions. In reality, this can enhance the ride comfort of the driver. Especially, the HAC-PP provides good tracking performance with the error in range of the defined boundary and the HAC-IFV can reduce the convergence time compared with two comparative adaptive controllers. It is finally remarked that the development of a new hybrid adaptive controller needs to be connected with desired control perfor-

Robust Adaptive Controls of a Vehicle Seat Suspension System

http://dx.doi.org/10.5772/intechopen.71422

21

This research was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.01-2017.28. The financial support is gratefully

\*

1 MediRobotics Laboratory, Department of Mechatronics and Sensor System Technology,

2 Smart Structures and Systems Laboratory, Department of Mechanical Engineering, Inha

Figure 9. Control results with the HAC-IFV at the driver (x1): (a1, a2) random step wave road, (b1, b2) regular bump road.

Figure 10. Sliding surface motion of the HAC-IFV (s): (a) random step wave road, (b) regular bump road.
