## 3 Experimental Scenario  
The experiment was conducted in such a scenario; As shown in Figure 2. We have designed the road in the CarMaker simulator using the road editor. The scenario includes two different road conditions such as a straight road 700 m in length, a downhill road characterized by a height of 26.8 m, a length of 100 m, and an angle of declination \(\theta=0.26\) rad, and a second straight road 1084 m in length. The selected slope for the downhill segment was chosen to reflect a practical gradient commonly encountered by standard vehicles during downhill driving.  
Figure 3 describes the experimental real scenario from CarMaker. The first screenshot is when the vehicle started in a straight line and after moving for about 700 m, then the vehicle entered a downhill road. The downhill road was 100 m long by 26.8 m wide. When the vehicle finishes downhill, it enters the second straight road.  
Figure 2: Conceptual visualization of experimental scenario.  
Figure 3: Visualization of the experimental test with CarMaker: At about 6 (s), the car is driving on a straight road. At about 38.5 (s), the road starts to go downhill. At about 44.5 (s), the downhill ends.  
To validate the proposed control algorithm, we implemented it in the CarMaker (ver. 12.0.1) simulator environment and MATLAB/Simulink (ver. 2022b). We have validated this algorithm on a Sonata passenger car that is front-wheel driven and uses gasoline. We performed our test on two different road conditions of two lanes (one in each direction), which are straight-line, and downhill road scenarios as shown in Figures 3 and 4. The upper-level controller is the control input \(\hat{u}=u_{d}\), which is the vehicle's desired acceleration, and is given to the experiment vehicle as shown in Figure 4. Table 1 describes the test vehicle parameters we used during the experiment.  
Additionally, the system response at the lowest value also suffers a transient response overshoot of around 5% and takes more time to settle down compared to optimal value. We noticed that with a smaller gain, the system response becomes slower but the vehicle settles down to the desired state as soon as the transient response ends with an adequately zero transient response overshoot and a very fast settling time at the optimal value. We can see that the high accuracy asymptotic output tracking is achieved. Let us remember our scenario is non-linear yet the tracking performance is performed well even when it is on the downhill road seen around 38.5-44.5 s, this result proves the fact that the super twisting algorithm is robust to parameter uncertainty and external disturbances during the sliding phase.  
The proposed method achieves the optimal value quickly, as shown in Figure 4(a), highlighting its superior performance. In Figure 4(b), the acceleration response mirrors the  
Figure 5: Tracking performance of the proposed system: vehicle velocity, acceleration, and control input under parameter variations.  
velocity response, but high gain causes unpleasant deceleration during 5.5-9.5 s, leading to potential passenger discomfort and oscillations during the downhill phase. At the optimal value, acceleration is smoother. Figure 4(c) shows that high gain induces oscillations in the control input, making it undesirable. However, performance improves significantly at the optimal parameter value.  
In Figure 6 the response of the vehicle pitch and pitch velocity is presented. The response appears to have similar characteristics with the velocity, meaning when the parameter value increases, the vehicle pitch tilts up and down faster and this movement impacts the riding comfort and stability unpleasantly. As a result, the high-pitch velocity can make a vehicle feel unstable, especially during sudden start and stop. In contrast, the result shows that at the optimal value, the pitching is smoother and passenger-friendly; consequently, the pitching velocity is slow and comfortable for the rider.