## 4 Simulation Experiment
### Experiment 2: Simulation of Longitudinal Dynamic Control of Electric Forklift
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Name** & **-** & **Parameter Name** & **-** \\ \hline Forklift model & EFG-BC/320 & Control method & iFFDL-MFA-PID \\ Maximum speed & 18 km/h & Load capacity & 2000 kg \\ Overall length & 3096 mm & Power system & Electric drive (48 V) \\ System parameter & \(i_{\mathrm{g}}=3.95\), \(C_{\mathrm{D}}=0.75\), \(k_{\mathrm{b}}=1.23\), \(A=1.85\) & Control parameter & \(\mu=0.9\), \(\rho=0.1\) \\  & \(f=0.05\), \(m=3820\) kg & & \(\partial=0.25\), \(K_{1}=0.35\) \\  & & & \(k_{2}=0.2\), \(K_{3}=0.01\) \\ Input and output data & Speed, position, and driving-force sensors & Control accuracy & \(\pm 0.132\) m/s (velocity tracking error) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: EFG-BC/320 electric balanced forklift (Jungheinrich Company, Shanghai, China) and iFFDL-MFA-PID parameters. (2) MSE \[\text{MSE}=\frac{1}{T}\sum_{k=1}^{T}\left|I_{d}-I(k)\right|^{2}\] (53)  
Furthermore, the following performance indicators were introduced to evaluate the iFFDL-MFA-PID, FFDL-MFAC, and PID methods. Table 3 presents the control performance of these three control methods. The calculation method for the performance indicators is shown in (52) and (53), where \(k\) and \(T\) represent the current sampling time and total time, respectively. The settling time is an important indicator of a control system's performance. In this study, we observed the response curve of the system when the reference signal changed at the 50 th second to identify the time point at which the output first reached and remained within a certain range of stability under the influence of the input. From Table 3, it is evident that the settling time of the iFFDL-MFA-PID method was approximately 7 seconds, which was less than half of the settling time of the MFAC method and significantly lower than that of the PID method. The iFFDL-MFA-PID method achieves an MAE of \(1.14\times 10^{-2}\) and an MSE of \(1.48\times 10^{-4}\), whereas the MFAC method yielded an MAE of \(3.26\times 10^{-2}\) and an MSE of \(8.62\times 10^{-4}\). These values are much smaller than those of the PID method, indicating higher precision and better stability. The results demonstrate that the control strategy proposed in this paper can more effectively suppress the harm caused by measurement disturbances to the system's stability, thereby achieving more accurate tracking of the system output. Figure 9 shows the control force (driving force/braking force) variation curves of the electric forklift under the action of the iFFDL-MFA-PID, FFDL-MFAC, and PID methods. As shown in the figure, the control forces of the electric forklift under the FFDL-MFAC and PID methods changed frequently and were greatly affected by interference. The control force change using the iFFDL-MFA-PID method was relatively stable, and the amplitude was smaller than that of the FFDL-MFAC method. This ensures the operational safety of the electric forklift and that no rollovers or other phenomena occur during the handling process. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **PID** & **FFDL-MFAC** & **iFFDL-MFA-PID** \\ \hline Adjust time (s) & 35 & 20 & 7 \\ MAE & \(5.67\times 10^{-2}\) & \(3.26\times 10^{-2}\) & \(1.14\times 10^{-2}\) \\ MSE & \(2.15\times 10^{-3}\) & \(8.62\times 10^{-4}\) & \(1.48\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Control schemes’ performance indexes. Figure 9: Electric forklift control force curves. Figure 10 shows the acceleration variation curves of electric forklifts using iFFDL-MFA-PID, FFDL-MFAC, and PID methods. As shown in the figure, the acceleration changes using the FFDL-MFAC and PID methods were too fast. In contrast to the iFFDL-MFA-PID method, the acceleration of the electric forklift changed slowly, which ensures the safe operation of the electric forklift and that there is no rollover in the handling process.