## 4 Simulation and Results  
In order to demonstrate the effectiveness of the control method of the NIMV system, the simulation model was built for the boom system. Figure 11 describes the co-simulation between the LMS AMESim (2020) and the MATLAB software (2017), in which the model components are represented in different color blocks and shown as follows: the hydraulic components are illustrated in blue blocks, the mechanical parts are depicted in the green blocks and the red blocks are the control signal ports. The setting parameters of the NIMV system for the AMESim model are shown in Table 4. Moreover, the simulation results are compared with the previous study to prove the effectiveness of the proposed control method based on tracking performance and energy consumption. Figure 11: The interface co-simulation of the NIMV system. Figure 10: Overall control strategy of the NIMV system for the boom excavator. The co-simulation is designed with two driving cycles that are used to test the performance of the NIMV circuit along with four working modes. During the operation, the external force of the boom cylinder which mimics the weight of the boom system is changed from 70 kg to 1000 kg, and the velocity is adjusted from 0.1 m/s to 0.2 m/s. Figure 12 illustrates the tracking performance of the proposed control method (VLF + FLC) compared with the previous method (VF + PID) on four metering modes (PE, PR, HSRE, and LSRR). In detail, the PE mode operates from 2 to 7 s with a velocity of 0.1 m/s and the load varies from 500 kg to 1000 kg (shown in Figure 12a), the PR mode retracts the cylinder from 9 to 12.5 s at 0.143 m/s in the changed load from 100 kg to 70 kg. While from 14 to 16.5 s is the HSRE mode, which extends at the velocity of 0.2 m/sec with the effect of loads from 100 kg to 150 kg, and the final is the LSRR mode which moves the cylinder down under the loads from 1000 kg to 500 kg at the velocity 0.125 m/s from the time 19 to 23 s. Under the same variable load, the displacement and velocity results of the proposed method have better performance and higher tracking precision than the VF + PID method, especially in the PE, PR, and LSRR modes (as shown in Figure 12b,c). In this case, the tracking precision is considered based on the root means square error (RMSE) method that is applied to analyze the displacement error on both methods, as shown in Table 5. The RMSE method can be calculated by Equation (23) provided below. \[RMSE=\sqrt{\sum_{i=1}^{n}\frac{e_{i}^{2}}{n}} \tag{23}\]  
The comparisons of the valve control signal and system pressure in the two methods are shown in Figure 13. In the valve control signal, both methods have the same signal at the \(K_{sa}\) valve, but the difference is mostly shown in the \(K_{ab}\) and \(K_{bt}\) valves. In PE mode the \(U_{bt}\) signal of the VLF + FLC method is smaller but controls the system better than the VF + PID method. The \(U_{ab}\) signal of the VLF + FLC method is smooth in LSRR mode, while the signal in the VF + PID method is high in fluctuation. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Components** & **Specification** & **Value** \\ \hline \multirow{4}{*}{Cylinder} & Bore chamber & 40 mm \\  & Rod chamber & 20 mm \\  & Length of Stroke & 500 mm \\  & Viscous friction coefficient & 2000 N/(m/s) \\ \hline \multirow{4}{*}{Pump} & Displacement & 8.3 cc/rev \\  & Max. speed & 1500 rpm \\  & Volumetric efficiency & 0.9 \\  & Torque efficiency & 0.95 \\ \hline Relief valve & Cracking pressure & 100 bar \\ \hline \multirow{4}{*}{Proportional valve} & Max. signal control & 10 Voltage \\  & Max. flow rate & 26.5 L/min \\  & Corresponding pressure drop & 10 bar \\ \hline \multirow{2}{*}{Directional valve} & Max. flow rate & 60 bar \\  & Corresponding pressure drop & 10 bar \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The setting parameter of the NIMV system.