# A Robust Intelligent Controller for Autonomous Ground Vehicle Longitudinal Dynamics
## 4 Results and Discussion  
The performance of the proposed strategy was evaluated by tracking a speed scenario while accounting for unknown disturbances and uncertainties. A comparison with the super-twisting SMC [12] was made in this context. Since the tire is the primary ground contact, the parametric uncertainty considered in this simulation was 50% and acted on the front-wheel moment of inertia (\(l_{\mathcal{W}}\)) [10; 43]. Moreover, the disturbance's nature was random and frequent. The vehicle parameters used were similar to [12]. The proposed control scheme settings were given as follows: \(\mathfrak{p}=0.001\), \(o=0.0001\), \(q=100\), \(a_{1}=15\), \(a_{1,2}=0,5\), and \(n=6\). All simulations were performed using MATLAB R2021a software, with a fixed sample time of 10 ms and an automatic solver on a Lenovo machine characterized by a 2.7 GHz processor, 16 GB of RAM, and a 512 GB SSD. Figure 5: The overall strategy that is suggested. The simulation outcomes of the proposed method and that of [12] are presented in Figures 6 and 7. In Figure 6, it can be observed that the suggested longitudinal controller directed the vehicle speed to perfectly reach the desired speed. However, at first sight, the simulation results of the super-twisting SMC approach were not as satisfactory as the proposed approach. To further analyze the performance of both approaches, it was important to study the results in transient and steady states. Indeed, in the transient regime the proposed approach showed zero rise time, whereas the response time was extremely insignificant. However, for the super-twisting SMC the rise time and the response time were highly  
Figure 6: Speed profile tracking responses. Figure 7: Controller output. significant and the overshoot was considerable, even in the steady state, particularly in the speed range, indicating the onset of slow motion. Moreover, a quantitative study was undertaken to underline the offered method's success utilizing the integral of the absolute error (iae), as written in Equation (37), as a performance index of the absolute error of the longitudinal displacement. These numerical values are presented in Table 1.  
\[\text{i}\alpha=\int_{0}^{t_{f}}|\;e|dt \tag{37}\]  
where \(t_{f}\) indicates the final simulation time. Figure 7 shows the engine torque acting on the wheel; this parameter exactly indicates the controller output. In fact, it is obvious that, at each speed step, the discussed control structure reacted simultaneously by imposing a torque that caused the vehicle's wheels to turn. In the acceleration steps, the torque resulting from the proposed method and that resulting from the super-twisting SMC did not occur in an increasing sense. As can be seen, the torque reached its maximum in the second speed step, and then decreased, returning to a lower value, even when the requested speed in the next step was higher than in the previous step. It can be stated that the controllers reacted intelligently by adding or subtracting the requested quantities to achieve the desired speed. Nevertheless, when the speed decreased, the controllers reacted in a decreasing rhythm, which is logical since the vehicle started to reduce its speed. The execution of the orders issued by the control algorithm was performed by the actuators, requiring sufficient energy for their operation. To this end, a comparative study gave numerical data regarding the energy consumption of the control strategies involved in this study. The integral of the square value (\(ISV\)) of the absolute error of the longitudinal acceleration provided this information related to the energy consumed by the acceleration/braking actuators [43]. The \(ISV\) is expressed in Equation (38). These results are illustrated in Table 2.  
\[ISV=\int_{0}^{t_{f}}|e_{acc}|^{2}dt \tag{38}\]  
Table 2 also shows that the proposed approach is optimal in terms of the power usage by the actuators moving the vehicle forward and backward and braking. **Remark 3**.