# Adaptive Cruise Control for Eco-Driving Based on Model Predictive Control Algorithm
## 3 Results and Discussion  
The simulation test bench is established to evaluate the performance of the proposed multiple objectives optimization strategy for the adaptive cruise control system. The simulation and comparison are conducted separately by two distinct control algorithms. The first one is the proposed MPC-based ACC system, considering the eco-driving assessment indicator fuel economy and other objectives, including driving comfortability, safety, and car-following. The other one is the ACC system based on the classic PID controller, which is only considering the car-following objective. An apparent difference between the PID controller and MPC controller is that the classic PID controller features in constant gains. In contrast, the MPC controller regulates the velocity of the host vehicle, while maintaining a strict safe distance constraint, which means that the MPC controller is capable of applying more aggressive maneuvers when the environment changes suddenly. The inter-distance from the host vehicle to the preceding vehicle is regulated strictly so that it is equal or greater than the critical minimum distance, which is regarded as the demand for driving safety. The magnitudes of acceleration and jerk are used to assess operating comfortability and fuel economy. The input to the emission and fuel consumption model is the speed profile data of host ACC-equipped vehicle, and the exhaust emission rate maps are plotted using instantaneous speed and acceleration data. Ultimately, the vehicle fuel economy is estimated. Figure 5: Simulation test bench. Figure 6: Structure of proportional-integral-derivative (PID) controller for ACC system. Two typical simulation driving scenarios are defined and used in this study:  
Scenario 1: Following a preceding vehicle with varying speed;  
Scenario 2: Following the changing preceding vehicles with a cut in and cut out behaviors. Generally, most integrated and complicated traffic scenes constitute the above two basic traffic scenarios. The related input parameters used in the simulation model are listed in Table 1.  
The first scenario of tracking a preceding vehicle with varying speed is the most typical traffic scene in a real driving situation. The speed profile for the preceding vehicle is reasonably generated. From Figure 7, it is noted that the host vehicle's speed responses to the predefined velocity of the preceding vehicle for both the PID-based ACC system and the MPC-based ACC system perform well. The cruise speed for the ACC system is set by the driver as 21.5 m/s. The driving comfortability assessment index, the acceleration, is presented in Figure 8, from which it can be observed that the MPC-based ACC system possesses a relatively smoother response than the PID-based ACC system. Figure 9 shows that both the PID-based and MPC-based ACC systems can follow the preceding vehicle actively without any accident, because the safe spacing is never exceeded the limit. Therefore, the performance of tracking and driving safety can be ensured for both two controllers. Table 2 shows the results of HC, CO, CO\({}_{2}\) and NO\({}_{\text{X}}\) emissions for both models in Scenario 1. Figure 10 shows that, the MPC-based ACC system can achieve about 12% improvement in fuel economy in Scenario 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Symbol** & **Values** & **Units** & **Symbol** & **Values** & **Units** \\ \hline \(T_{s}\) & 0.1 & s & \(p\) & 16 & – \\ \(R\) & 760 & m & \(c_{h}\) & 5 & – \\ \(m\) & 1575 & kg & \(v_{\text{min}}\) & 0 & m/s \\ \(I_{z}\) & 2875 & m\textbackslash N-s  
Figure 8: Acceleration response in scenario 1. Figure 7: Speed response in scenario 1. Figure 9: Spacing response in scenario 1. In scenario 2, which is about following the changing preceding vehicles with cut in and cut out behaviors, the ACC-equipped host vehicle operates along a predefined road section. At the outset, the host green vehicle follows a preceding red vehicle.