## 5 Results of Simulation
The bottom graph shows that the proposed controller effectively suppresses high-frequency noise compared to MRAC, particularly between 40 s and 60 s. This indicates smoother and more stable control inputs. Moreover, MRAC exhibits a peak jerk value of approximately 1.0 m/s\({}^{3}\) during the acceleration phase, while the proposed controller maintains a lower peak jerk of about 0.8 m/s\({}^{3}\). This clearly demonstrates improved smoothness in control action. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Road Grade** & \multirow{2}{*}{**Payload Condition**} & **Sudden Headwinds** \\  & **[+0.67\({}^{\circ}\)]** & & [\(-\)20, \(-\)30 m/s] \\ \hline \hline  & \(\mathrm{O}\) & \(\mathrm{X}\) & \(\mathrm{X}\) \\  & \(\mathrm{O}\) & \(\mathrm{X}\) & \(\mathrm{O}\) \\  & \(\mathrm{O}\) & \(\mathrm{X}\) & \(\mathrm{O}\) \\  & \(\mathrm{O}\) & \(\mathrm{X}\) & \(\mathrm{O}\) \\  & \(\mathrm{O}\) & \(\mathrm{X}\) & \(\mathrm{O}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Scenario conditions. In the second scenario, where sudden headwinds occur, the top graph in Figure 8b shows that the LQR, MRAC, and proposed controllers successfully reach the desired speed. However, as seen in the middle graph in Figure 8b, a slight acceleration limit occurs during the control process. This finding indicates that actuator saturation begins to appear in this scenario; however, it does not significantly hinder overall speed tracking. In contrast to the ideal condition in Scenario 1, the reference and modified reference models diverge slightly due to the imposed acceleration limit. As shown in the bottom graph in Figure 8b, the proposed controller demonstrates reduced jerk responses compared to the MRAC. Specifically, the peak jerk value of the standard MRAC reached approximately 0.9 m/s\({}^{3}\), while the proposed controller achieved a lower maximum jerk of around 0.7 m/s\({}^{3}\). Moreover, during the 40-60 s period, the standard MRAC exhibited noticeable high-frequency oscillations, whereas the proposed controller effectively suppressed them, indicating enhanced control smoothness and stability. In the third scenario, where the actuator limit occurs, the top graph in Figure 9a shows that both the LQR controller and the standard MRAC cannot reach the desired speed between 70 s and 110 s. This error is likely due to a lack of control input caused by the acceleration limit. As seen in the middle graph of Figure 9a, the reference model reduces the acceleration-control input before the vehicle reaches the target speed. In contrast, the proposed control system successfully reached the desired speed. This is because the modified reference model (which accounts for the vehicle's acceleration limit) continues to apply acceleration input even when the vehicle has not yet reached the desired speed. As shown in the bottom graph of Figure 9a, the standard MRAC shows consistently higher peak jerks compared to the proposed control system throughout the acceleration  
Figure 8: (**a**) Simulation results for Scenario 1; (**b**) simulation results for Scenario 2.  
phase--with a maximum jerk of approximately 0.7 m/s\({}^{3}\). In contrast, the proposed control system reaches a significantly lower maximum jerk (0.6 m/s\({}^{3}\)). Noticeable oscillations are observed in the standard MRAC during the 50 to 60 s period, while the proposed control system effectively suppressed these oscillations, which indicates improved stability. In the fourth scenario, where a more severe actuator limit occurs, the top graph in Figure 9b shows that both the LQR controller and standard MRAC struggle to reach the desired speed over time. This error is also likely due to a lack of control input because of the acceleration limit. In this case, the proposed control system also successfully reached the desired speed. As seen in the middle graph of Figure 9b, the vehicle's acceleration does not exceed 0.5 m/s\({}^{2}\), and in the case of standard MRAC, the lack of acceleration prevents the vehicle from reaching the target speed.