# Driving Safety Improved with Control of Magnetorheological Dampers in Vehicle Suspension
## 4 Simulation Results
### Test Procedure  
In each experiment, two types of driving methods were tested, i.e., road manoeuvres (accelerating or braking) or constant vehicle speed. Figure 8 presents time diagrams of vehicle longitudinal velocity. The first group of simulation was performed for the vehicle that alternately accelerates, drives and brakes, whereas the overall time of the simulation is equal to approximately 300 s. Ten cycles of such a driving strategy were simulated for each case. The second group of simulation experiments was dedicated to the vehicle moving with a constant speed after a single accelerating, which is finished by a single braking. Drive and braking systems of the vehicle were disabled during this phase and the vehicle was assumed to be towed while using a rigid connection by another vehicle with ideal stabilization of longitudinal (\(x\) direction) velocity. An alternative approach can be based on the implementation of an additional cruise control algorithm in the implemented model. However, it was not considered in the presented manuscript. An assumption about constant vehicle speed is important for standard validation of vibration control algorithms, since effective vibration excitation that is induced by road unevenness is strictly \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Road profile and simulation parameters**} \\ \hline \(f_{ts}=1000\) Hz & \(f_{ps}=1000\) points m\({}^{-1}\) & rc (road class) = F & \(a_{H}=6.6\) m \\ \hline \multicolumn{4}{c}{**4 DoFs half-car suspension model**} \\ \hline \multicolumn{4}{c}{\(m_{s}=171.5\) kg} & \(I_{sp}=74.3\) kgm\({}^{2}\) \\ \hline \(l_{f}=0.609\) m & \(l_{r}=0.681\) m & \(h_{s}=0.554\) m \\ \hline \(k_{sf}=22.208\) kNm\({}^{-1}\) & \(k_{sr}=34.857\) kNm\({}^{-1}\) & \(c_{sf}=300\) Nsm\({}^{-1}\) & \(c_{sr}=300\) Nsm\({}^{-1}\) \\ \hline \multicolumn{4}{c}{_Tanth based model of the MR damper_} \\ \hline \(i_{intr}\in(0.0;1.33)\) A & \(\alpha_{0}=62.42\) N & \(\alpha_{1}=1340\) N\(\sqrt{\text{A}^{-1}}\) \\ \hline \(\beta=39.96\) sm\({}^{-1}\) & \(c_{0}=802.8\) Nsm\({}^{-1}\) & \(c_{1}=488.5\) Nsm\({}^{-1}\)\(\sqrt{\text{A}^{-1}}\) \\ \hline \multicolumn{4}{c}{**Wheel and tire models**} \\ \hline \(m_{uf}=10\) kg & \(m_{ur}=15\) kg & \(I_{uf}=0.6\) kgm\({}^{2}\) & \(I_{ur}=0.9\) kgm\({}^{2}\) \\ \hline \(r_{uf0}=0.317\) m & \(r_{ur0}=0.317\) m & \(A_{uf0}=0.244\) m\({}^{2}\) & \(A_{ur0}=0.244\) m\({}^{2}\) \\ \hline \(p_{uf0}\cdot w_{uf}=5234.1\) Nm\({}^{-1}\) & \(p_{ur0}\cdot w_{ur}=5113.6\) Nm\({}^{-1}\) & \(c_{Af}\cdot w_{uf}=447.3\) Nsm\({}^{-2}\) & \(c_{Ar}\cdot w_{ur}=560.4\) Nsm\({}^{-2}\) \\ \hline \multicolumn{4}{c}{**Burckhardt model of tire to road friction for wet concrete surface**} \\ \hline \(f_{b0}=0.4004\) & \(f_{b1}=33.7080\) & \(f_{b2}=0.1204\) \\ \hline \multicolumn{4}{c}{**Rolling resistance for concrete surface and aerodynamic drag**} \\ \hline \multicolumn{4}{c}{\(f_{\text{roll}}=0.008\)} \\ \hline \(\rho_{\text{air}}=1.223\) kgm\({}^{-3}\) & \(c_{\text{air}}=0.72\) & \(A_{\text{air}}=1.75\) m\({}^{2}\) \\ \hline \multicolumn{4}{c}{**Parameters of front braking and rear drive systems for half-car model**} \\ \hline \multicolumn{4}{c}{\(t_{b}=160\) Nm} & \(t_{e}=225\) Nm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the vehicle model and its submodels. dependent on the vehicle speed while assuming the same road profile. It can be stated for the first order derivative of vertical road-induced excitation, as follows:  
\[v_{rz}=\frac{dz_{r}}{dt}=\frac{dz_{r}}{dx_{r}}\cdot\frac{dx_{r}}{dt}=\frac{dz_{r}} {dx_{r}}\cdot\frac{dx_{s}}{dt}=\frac{dz_{r}}{dx_{r}}\cdot v_{sx}, \tag{30}\]  
where \(v_{rz}\) denotes road-induced excitation in \(z\) direction with respect to time. The results obtained for the phase of constant speed were analysed in the frequency domain \(f\) based on power spectral density (PSD) characteristics \(S_{x}(f)\). The PSD was calculated for all signals while using the _pwelch_ function available in Matlab/Simulink environment.