# Adaptive Cruise Control for Intelligent City Bus Based on Vehicle Mass and Road Slope Estimation
## 4 Simulation and Experiment Results
### Simulation Results  
In this section, the simulation results of proposed strategy MPC + EKF are analyzed as follows. The simulation results of the longitudinal speed are shown in Figure 9. It can be seen that there are several sudden changes of the preceding vehicle speed and the current vehicle controlled by MPC + EKF strategy follows the preceding bus very well. From Figure 5, we know the following distance is related to the vehicle speed, so the shape of the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbol** & **Value** \\ \hline Predictive horizon & \(p\) & 8 \\ Control horizon & \(m\) & 1 \\ Optimal distance efficient & \(\alpha\) & 0.4 \\ Distance cost efficient I & \(k_{I}\) & 200 \\ Distance cost efficient II & \(k_{2}\) & 100 \\ Distance cost efficient III & \(k_{3}\) & 1000 \\ Speed cost efficient & \(k_{4}\) & 50 \\ Acceleration cost efficient & \(k_{5}\) & 100 \\ Jerk cost efficient & \(k_{6}\) & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Figure 8: The changes of vehicle mess and road slope. Figure 7: The longitudinal speed of the preceding vehicle. following distance shown in Figure 10 is coincidentally similar to the vehicle speed. It can be seen that throughout the ACC process, the actual following distance is always between the maximum and minimum safe following distances. It means the proposed MPC + EKF strategy can guarantee the tracking ability and driving safety of ACC. As a comparison, the speed of the current vehicle without the EKF strategy is also shown in Figure 9. It can be clearly divided into three zones. At the first zone, the estimated speed without EKF can follow the preceding vehicle but not well because the road slope has changed and the mass has not changed. At the second zone, the estimating speed without EKF is far below the preceding vehicle speed, because the vehicle mass has increased to 18 tons while the mass in the vehicle dynamics model is still 14 tons (the mass is not estimated and it is a constant), so the EM torque is not enough to increase the speed to the preceding vehicle's speed. At the third zone, the vehicle mass has reduced to 12 tons, opposite to the second zone, the EM torque is too large, causing the vehicle speed to overtake the preceding vehicle severely. Therefore, without the estimation for vehicle mass and road slope, the tracking ability and driving safety in ACC is hard to achieve. Figure 10: The following distance of preceding vehicle and current vehicle. Figure 9: The simulation results of the longitudinal speed. As shown in Figure 11, The traveling distance of preceding and current vehicles is about 8.1 km. During the ACC process, the actual traveling distance of the current bus is always smaller than the preceding one. The distance between the two buses is shown in Figure 12, it can be seen that the distance is almost within the safety zone. That is, the following distance meets the safety demand. Figure 11: The traveling distance of preceding vehicle and current vehicle. Figure 12: The traveling distance between preceding vehicle and current vehicle. The reduction of battery SoC means energy consumption, meanwhile, as described in Section 2.2, when EM works as a generate. Therefore, we measure vehicle energy efficiency by how much \(SoC\) is reduced. In this paper, the parameters of the preceding vehicle are the same as those of the current vehicle. Figure 14 shows the change of \(SoC\) by time during ACC process. It can be seen that the SoC of the preceding vehicle reduced from 65 to 61% and that of the current vehicle reduced from 65 to 62%. The current vehicle saved about 10% energy compared to the preceding vehicle in per 100 km. This is because when under the control of MPC + EKF strategy, the jerk of current bus results in smaller changes than that of the preceding bus. Figures 15 and 16 show the results of vehicle mass estimation and road slope estimation obtained by EKF. The estimated results have errors with the real values, but the trends are the same.