## 4 Simulation Studies
### Full Car Model Simulation  
A full car dynamic model that had eight degrees-of-freedom including roll, pitch, heave, driver seat, and four wheel vertical motions was simulated for more realistic vehicle behavior. Table 2 shows the model parameters of the vehicle under advanced development with in-wheel motors on the rear axle. In order to evaluate the performance variation for the change in damping coefficient, a simulation was performed for the damping coefficients listed in Table 3. Note that the fourth passive damping coefficient in Table 3 was the same as the passive damping coefficient in Table 2.  
Figure 7: RMS of suspension stroke. (**a**) smooth road; (**b**) rough road. Figures 8-10 show the cross plots for the RMS driver seat heave, chassis pitch, and chassis roll accelerations against RMS tire normal force variation (road-holding performance), respectively. The performance measures were frequency-weighted performance indices computed by multiplication of frequency-weighted curves (Figures 11 and 12) as suggested by ISO2631 [7] with RMS heave, pitch, and the value of roll accelerations and RMS tire normal force variation. The RMS values were calculated using 1/3 octave band frequencies of frequency responses, which were obtained from the time-domain simulation of the full car dynamics model with nonlinearities over the road conditions described in the simulation conditions. In the figures, the solid line denotes the double sky-hook case, the dashed line denotes the conventional sky-hook, and the dash-dot line represents a passive damper. The numbers in each plot correspond to the different damping coefficients listed in Table 3. Note that in the case of the double sky-hook algorithm, the value of \(B1_{sky}\) was fixed to the value of 10,000 Ns/m and the simulation was performed for the values of \(B2_{sky}\) from zero (this point in Figures 8-10 is point 2 in the conventional sky-hook algorithm) to the values in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Effective weight of front wheel (\(m_{\textit{atf}}\), \(m_{\textit{atf}}\)) & 54 kg \\ Effective weight of rear wheel (\(m_{\textit{atf}}\), \(m_{\textit{atf}}\)) & 68 kg \\ Weight of sprung mass (\(m_{\textit{s}}\)) & 1754 kg \\ Pitch moment of inertia (\(J_{\phi}\)) & 3012 kg m\({}^{2}\) \\ Roll moment inertia (\(J_{\theta}\)) & 598 kg m\({}^{2}\) \\ Front axle location from C.G. (\(L_{\textit{r}}\)) & 1.44 m \\ Rear axle location from C.G. (\(L_{\textit{r}}\)) & 1.56 m \\ Left/Right side from C.G. (\(W_{\textit{l}}\), \(W_{\textit{r}}\)) & 0.82 m \\ Front spring stiffness & 24,426 N/m \\ Rear spring stiffness & 31,954 N/m \\ Front passive damper coefficient (effective) & 1400 Ns/m \\ Rear passive damper coefficient (effective) & 2000 Ns/m \\ Suspension friction & 54 N \\ Front stabilizer bar stiffness & 19,994 N/m \\ Rear stabilizer bar stiffness & 10,204 N/m \\ Tire vertical stiffness & 248,000 N/m \\ Tire vertical damping coefficient & 322 Ns/m \\ Weight of driver (\(m_{d}\)) & 65 kg \\ Driver’s seat stiffness & 10,507.1 N/m \\ Driver’s seat damping coefficient & 875.6 Ns/m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model parameters for a full car. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Passive Damping**} & \multicolumn{2}{c}{**Sky-Hook**} & \multicolumn{2}{c}{**Double Sky-Hook**} \\  & \multicolumn{2}{c}{**(Ns/m)**} & \multicolumn{2}{c}{**Algorithm**} & \multicolumn{2}{c}{**Algorithm**} \\  & **Front** & **Rear** & \(B1_{sky}\) (Ns/m) & \(B2_{sky}\) (Ns/m)** \\ \hline
1 & 560 & 800 & 5000 & 500 \\
2 & 840 & 1200 & 10,000 & 1000 \\
3 & 1120 & 1600 & 40,000 & 1500 \\
4 & 1400 & 2000 & 100,000 & 2000 \\
5 & 1680 & 2400 & 1,000,000 & 2500 \\
6 & 1960 & 2800 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Damping coefficients. Figure 8: Tire normal force variation vs. heave acceleration. Figure 10: Tire normal force variation vs. roll acceleration. Figure 9: Tire normal force variation vs. pitch acceleration.