## 4 Simulation and Results
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Mode** & **VLF + FLC** & **VF + PID** \\ \hline PE & 0.776 & 1.766 \\ PR & 0.369 & 9.082 \\ HSRE & 3.694 & 3.563 \\ LSRR & 0.351 & 14.466 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Root means square error for metering modes on both control methods. Figure 12: Comparison of the tracking precision of both methods under variable load. (**a**) The variable load applied to the cylinder, (**b**) the velocity, (**c**) the displacement, and (**d**) the displacement error. Figure 13: The comparison of (**a**) valve control signal and (**b**) pressure of the system on both methods. In addition to the high tracking precision, energy consumption is also one of the criteria to evaluate the effectiveness of the proposed control method. The energy consumption of the system can be calculated based on the energy consumption of the electric motor, which drives the main pump of the NIMV system, and is provided by Equation (24). \[E=\int T\omega dt \tag{24}\]  
where \(E\) is the energy consumption of the electric motor, \(T\) is the torque and \(\omega\) is the angular velocity which converts from the speed of the motor. Based on Equation (24), the comparison of the energy consumption of both control methods is provided in Figure 14. In addition, the detailed energy consumption of each metering mode is presented in Table 6. The result shows the energy consumption in the PE mode is the same, but the motor speed after 4.5 s of the VF + PID method fluctuates when changing the load. This is the limitation of the PID controller on the VF + PID control method when applying the variable load. Moreover, in PR mode, the energy consumption of the VLF + FLC (0.76 kJ) is higher than in the previous control method (0.12 kJ) by about 84% because the proposed method uses the energy to ensure reduction in the displacement error; therefore, the motion tracking precision of the proposed method is 95% higher compared with the previous method (shown in Table 5). In the HSRE mode, the VLF + FLC method consumes less energy (1.74 kJ), it achieves approximately 40% energy saving. The VFPB method is applied to the pump control while the VF + PID method (2.9 kJ) only uses the PB method. The \(p_{s}\) pressure at the HSRE mode on both control methods can be seen in Figure 13b, while the \(p_{s}\) of the VLF + FLC is decreased after 15 s, \(p_{s}\) of the VF + PID method maintain high pressure until the end of the mode, leading to energy loss via the relief valve. From all the above results, the proposed method can perform well in the metering modes of the NIMV system, not only ensuring high accuracy but also lower energy consumption. To prove the advantages of the proposed switching mode, some simulations with changing the load and velocity while the cylinder is in operation are carried out as shown in Table 7. Figure 15 describes the behavior of the switching mode in two operating cycles of the NIMV system. At switching points, a transient response occurs, which causes unstable and unsmooth switches in the system [18]. However, this problem is overcome by the proposed method. The load and target velocity are the two factors that are used in the control algorithm of the system; hence, when the switching mode takes place, the control signals are adjusted quickly to respond promptly to changes in the system. In conclusion, the proposed control method enhances the tracking precision not only in the variable load condition but also in the switching mode condition. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Mode** & **VLF + FLC** & **VF + PID** \\ \hline PE & 4.638 & 4.608 \\ PR & 0.76 & 0.12 \\ HSRE & 1.74 & 2.9 \\ LSRR & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Energy consumption on both control methods (k)).