## 5 Results  
This research uses MATLAB's Simulink and Simscape toolboxes to design the vehicle. Therefore, developing the optimization algorithm for the physical model is tricky. This research uses a system identification technique to estimate the mathematical model of the system in the frequency domain for the more straightforward implementation of the optimization algorithms. In this section, the simulation and experimental results for the VW Crafter's conventional and hybrid powertrains are presented. Table 10 presents the gains of the classical PID and the GA-PID and PSO-PI found based on the ITAE objective function. For GA-PID, \(K_{p}\), \(K_{i}\), and \(K_{d}\) were 70.6657, 0.3339, and 72.4406, respectively. For PSO-PI, \(K_{p}\) and \(K_{i}\), were 1243.1 and 1.3453, respectively. While Table 11 presents the gains of the FOPID controller. Figure 21 shows the achieved vehicle's speed due to the WLTP drive cycle. The vehicle speed has tracked the reference speed with a minimal deviation at some point due to the system complexity and approximation during the system's identification process. The performance of the proposed control strategy was found to be more effective than the PSO-PID and FOPID strategies in terms of the energy consumption and system's energy and power efficiency. However, it was found that the derivative part did not perform well in the system response due to noisy signals, which would take more time to converge to the optimal solutions. Therefore, a PSO-PI and FOPID control strategies were used to compare and verify the effectiveness of our proposed control algorithm (GA-PID). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Gain** & **Classical PID** & **GA-PID** & **PSO-PI** \\ \hline \(K_{p}\) & 60 & 70.6657 & 1243.1 \\ \(K_{i}\) & 10 & 0.3339 & 1.3453 \\ \(K_{d}\) & 60 & 72.4406 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Classical PID, GA-PID, and PSO-PI Gains. \begin{table}
\begin{tabular}{c c} \hline \hline
**Gains** & **Value** \\ \hline \(K_{p}\) & 1000 \\ \(K_{i}\) & 20 \\ \(K_{d}\) & 0.05 \\ \(lamda\)\([\lambda]\) & 0.5 \\ \(mu\) \([\mu]\) & 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Fractional order PID Gains. Figure 20: The hybrid Vehicle Model. Figures 22 and 23 show the power and energy consumed by the Nissan Leaf battery and the electric motor. However, the positive portion of the energy in Figure 20 represents the energy consumed, while the negative part due to the drive cycle represents the energy recovery. The energy consumption and recovery concept for an electrical machine was investigated by [PERSON] in [70]. For the GA-PID control strategy (with optimal control gains of 70.6657, 0.3339, and 72.4406), the energy consumed by the battery and motor was 0.1295 kWh/km (12.95 kWh/100 km) and 0.1162 kWh/km (11.62 kWh/100 km). The power consumed by the battery and motor was 50.80 kW and 44.94 kW. The energy and power efficiencies are approximately equal, which were 89.73% and 88.46%, respectively. Moreover, For the PSO-PI control strategy (with optimal control gains of 1243.1 and 1.3453), the energy consumed by the battery and motor was 0.1403 kWh/km (14.03 kWh/100 km)  
Figure 21: FW Crafter Speed due to WLTP test Procedure.The vehicle speed has successfully tracked the reference speed with a minimal deviation at some point. This is attributed to the system’s complexity and nonlinear nature. Figure 22: Electrical and Mechanical Power due to WLTP test Procedure. The red line represents the motor consumed power which stands at 50.80 kW peak. While the blue line represents the battery power which stands at 44.94 kW. Figure 23: Electrical and Mechanical Energy due to WLTP test Procedure. The electrical energy represents the battery consumed energy which is the red line in this case, and the blue line which represents the energy consumed by the PMSM. and 0.1228 kWh/km (12.28 kWh/100 km). The power consumed by the battery and motor was 55.06 kW and 48.61 kW.