## 5 Simulation Analysis  
In this section, simulations are carried out to verify the effectiveness of the proposed controllers. Closed-loop simulations with driver-vehicle-road model were designed and the comparisons between cars with AEBS on and off were analyzed under different working conditions. To evaluate the proposed AEBS algorithm, a simulation scenario is composed of an emergency deceleration case as follow: preceding vehicle speed: 80 km/h; subject vehicle speed: 50 km/h; initial clearance: 50 m; preceding vehicle's final speed: 30 km/h; warning time: 1.4 s. The results are shown in Figures 2-6. Figure 3: Comparison of relative distance. Figure 2: Comparison of relative speed. As shown in Figure 2, when the preceding vehicle starts to decelerate, the AEBS algorithm does not give a warning signal immediately, but the safety indexes meet the activation conditions as shown in Figures 5 and 6. Also, Figures 5 and 6 show comparisons of \(TTC^{-1}\) and \(WI\). As shown in Figure 3, the AEBS operates autonomous braking to avoid s rear-end collision. However, without the AEBS, the driver cannot prevent the vehicles' collision when the braking input is delayed. Figure 4 illustrates a comparison of dynamic response. It can be seen that the execution speed of EBS (brake by wire) is \(\sim 10^{-1}\). Figure 4: Comparison of vehicle acceleration. Figure 5: Comparison of \(TTC^{-1}\). Figure 6: Comparison of \(WI\). From the comparative analysis of Figure 7, it can be seen that the vehicle collision risk is reduced and the response time is increased after the increase in the vehicle distance. Therefore, the vehicle speed change is gentle and the driving comfort is improved for the vehicle with an AEBS system. However, for vehicles without an AEBS system, the vehicle speed variation is still large due to the delay in the braking response. As shown in Figure 9, with the AEBS system vehicle, the braking acceleration starts to gradually become gentle at about 12 s, and the vehicle braking shock becomes small. From the analysis available in Figure 10, after the increase in distance, for vehicles without AEBS function, vehicle safety indicators' return to the security zone speed is relatively rapid. In order to analyze the control characteristics of AEBS for static targets, the initial vehicle distance is 60 m, the initial vehicle speed is 50 km/h, and the front vehicle remains stationary. The warning time is 1.4 s, and the response is shown in Figures 12-16. Figure 11: Comparison of \(WI\). Figure 10: Comparison of \(TTC^{-1}\). Figure 14: Comparison of vehicle acceleration. Figure 12: Comparison of relative speed. Figure 13: Comparison of relative distance. As shown in Figure 12, with the AEBS function, the smart car braking response speed has obvious advantages. In the absence of the AEBS function, the vehicle cannot return to the stable zone even if the maximum braking acceleration is applied to the intelligent vehicle due to the relatively late execution of the vehicle control operation, as shown in Figures 15 and 16. In order to analyze the dynamic response characteristics of the AEBS system, the simulation scenario is a low-speed vehicle's cut-in situation. The details of the scenario are as follows: the initial vehicle distance is 20 m, and the intelligent vehicle initial speed is 80 km/h; the cut-in vehicle speed is 60 km/h and constant; the warning time is set to be 1.4 s. The compared results are shown in Figures 17-20. As shown in Figure 17, the vehicle with AEBS function can automatically control the vehicle to maintain safe running; without AEBS function, the vehicle can be stabilized within the appropriate delay response range. However, with AEBS function, the vehicle can be controlled earlier than without AEBS function.