## 5 Results of Simulation
This allows the performance difference to be attributed solely to structural improvements, such as the use of the state predictor and the input constraint handling mechanism, rather than to parameter tuning. In order to evaluate the longitudinal control performance of the HDV, the ability to reliably and accurately track the target speed is assessed under conditions that involve \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Value** & **Units** \\ \hline \(k_{x,0}\) & \([1.8257,\ 1.4817]^{T}\) & - \\ \(k_{r,0}\) & \([1.8257]^{T}\) & - \\ \(W_{0}\) & \([0,\ 0]^{T}\) & - \\ \(k_{u,0}\) & 0.3 & - \\ \(\Gamma_{x}\) & \(0.1\times I_{2\times 2}\) & - \\ \(\Gamma_{r}\) & 0.1 & - \\ \(\Gamma_{\beta}\) & \(0.01\times I_{2\times 2}\) & - \\ \(\Gamma_{u}\) & 0.1 & - \\ \(\delta\) & \(0.3u_{max}\) & - \\ \(\mu\) & 10 & - \\ \(\alpha\) & 10 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used in the control system. Figure 7: Road slope. model uncertainties, disturbances, and actuator limitations. This section analyzes the tracking performance of four different control systems using previously defined scenarios. The first system is the LQR controller, the second is the standard MRAC, and the third is the proposed control system. Furthermore, a comparison between the reference model of the standard MRAC and the modified reference model of the proposed control system demonstrates the adjustments made to account for actuator limitations. This analysis is facilitated by the simulation results from the four different scenarios presented in Table 3.  
Each simulation scenario incorporates physically meaningful external disturbances--road gradient, headwind, and payload variation--quantitatively modeled based on the force components introduced in Section 2. The road slope was defined with reference to the Korean Road Traffic Act to ensure that the simulated inclines reflected realistic road design standards. The payload variations (up to +100%) correspond to the typical maximum load conditions observed in HDV operations. In addition, headwind disturbances ranging from \(-20\) to \(-30\) m/s were included to simulate severe but physically plausible environmental conditions, such as those encountered during hurricane-level weather. These conditions are directly translated into gravitational, aerodynamic, and rolling resistance forces that influence the vehicle's longitudinal acceleration. This setup enables a comprehensive and realistic evaluation of how effectively the proposed closed-loop control system maintains robust speed tracking under complex and adverse operating conditions. Figures 8 and 9 show the results of the longitudinal speed-tracking performance for three different control strategies. The top graph in each figure displays the vehicle velocity. The second graph in each figure displays the vehicle acceleration, and the third graph in each figure displays the vehicle jerk. Figure 8a shows the first scenario, an ideal condition where no actuator limitations are observed. Figure 8b presents the second scenario, where sudden headwinds are applied, which cause slight actuator responses. Figure 9a shows the third scenario, where a payload of +9100 kg was added together with road grade and headwind disturbances, which led to clear signs of actuator saturation. Figure 9b depicts the most challenging scenario, involving a payload of +18,200 kg, together with road grade and headwind disturbances, where actuator limitations become more pronounced. In the first scenario, the top graph in Figure 8a shows that the LQR, MRAC, and proposed controller successfully track the reference input. Since no disturbances occur in this case, all controllers exhibit ideal speed-tracking performance. The middle graph confirms the absence of an acceleration limit, as actuator saturation does not appear, which results in smooth acceleration responses.