## 5 Semi-Active Control Analysis of the Multi-DOF Seat Damping Suspension
### Simulation of the Multi-DOF Seat Damping Suspension  
After inputting the vibrational excitation, the optimal fuzzy semi-active control method and the passive vibration-reduction method were used to simulate vibrations of the multi-dimensional damping seat platform. First, the GWO algorithm was applied to optimize the quantization factors \(K_{a}\) and \(K_{v}\), and the scale factor \(K_{u}\) of the fuzzy semi-active control. According to ISO-2631-1:1997 (E) [27], the six degrees of freedom of the center position of the upper platform of a damping seat had different weights on the comfort evaluation of the vehicle seat. In this study, the weights of translation along the x-, y-, and  
Figure 23: Simplified half-vehicle model of vehicle seat suspension.  
Figure 24: Semi-active control simulation model of multi-dimensional vibration-damping seat.  
Figure 25: The seat excitation input of control simulation. (**a**) vibration excitation 1 (**b**) vibration excitation 2.  
\(z\)-axes were all 1, rotation along the x-axis was 0.63, rotation along the y-axis was 0.4, and rotation along the z-axis was 0.2. Since the vibration input of this simulation involved the vertical, horizontal, and roll directions; that is, the translational direction along the \(y\)- and \(z\)-axes and the rotational direction along the \(x\)-axis, the optimization objective function was set as follows:  
\[a_{v}=\sqrt{a_{y}^{2}+a_{z}^{2}+0.63a_{rx}^{2}} \tag{21}\]  
where \(a_{v}\) is the optimization objective of the fuzzy control, \(a_{y}\) is the translational acceleration along the \(y\)-axis, \(a_{z}\) is the translational acceleration along the \(z\)-axis, and \(a_{rx}\) is the angular acceleration along the \(x\)-axis. After gray wolf algorithm optimization, the fuzzy control parameters \(K_{a}=6.88\), \(K_{v}=9.18\), and \(K_{u}=\)9.67 were obtained, and the vibration control simulation was carried out according to the parameters. The simulation output the acceleration in the vertical, horizontal, and roll directions of the upper and lower platforms on the seat damping suspension. The results are shown in Figures 26-28.  
The blue and red curves in Figures 26-28 show the acceleration results of the upper platform of the damping seat under passive damping and semi-active controlled damping, respectively, in three directions: rotation around the \(x\)-axis and translation along the \(z\)-axis and \(y\)-axis. The black curves in Figures 26-28 show the vibration acceleration signals of the lower platform of the damping seat in the three directions. The root mean square (RMS) values of the simulation results are shown in Table 4.  
Figures 26-28 show that under random displacement excitation, due to the low excitation frequency of the vibration, when the passive damping method was used, the maximum values of vibration accelerations of the upper platform rotating around the \(x\)-axis, translating along the \(z\)-axis, translating along the \(z\)-axis, and translating along the \(y\)-axis, appeared to be amplified in all three directions. After using the optimized fuzzy skyhook semi-active control method proposed in this paper, the vibration accelerations in all three directions were reduced. As can be seen from Table 4, when the passive damping method was adopted, the RMS values of the vibration accelerations were amplified in all three directions. After using the semi-active control method proposed in this paper, the angular acceleration, and the accelerations in the three directions of rotation around the x-axis, translation along the \(z\)-axis, and translation along the \(y\)-axis, were reduced by 25.3%, 13.4%, and 20.0%, respectively, compared with the passive damping method. Furthermore, after semi-active control, relative to the lower platform of the seat, the upper platform achieved vibration reductions in all three directions. Rotation around the \(x\)-axis, translation along the \(z\)-axis, and translation along the \(y\)-axis reduced vibrations by 9.4%, 8.9%, and 5.9%, respectively.