## 4 Simulation Study
### PI Parameter Online Tuning System-Positive Flow System  
In the variable speed quantitative pump positive flow system, an electronic control handle is used to achieve pilot signal control. Meanwhile, the output signal of the electronic control handle is converted to the target speed information of the main pump. The simulation process simulates a movement cycle of the boom cylinder of an 8-ton pure electric hydraulic excavator under typical cycle conditions.  
The output signal curve of the pilot handle is shown in Figure 12. The displacement curve of the actuator cylinder which is a typical movement cycle of the boom cylinder is shown in Figure 13. When the pilot signal output is 0, the motor to drive the main pump is in the idling stage and the cylinder does not move. At 1 s, the given boom-rise pilot output signal is 10 V. The boom cylinder extends at the highest speed with uniform speed. At 5.5 s, the boom-drop pilot output signal is linear to increase, and becomes constant at 6.5 s. The boom cylinder decreases at an accelerated speed first, and then decreases at a uniform speed. During the descent process, the shoveling and digging loading action is performed. After the shoveling action is executed, the boom cylinder is extended again. After the cylinder is fully extended, the slewing mechanism performed the revolving action and unloaded at the designated position.  
Figure 11: The torque change view when the load was suddenly loaded.  
Figure 10: The partial enlarged view of the speed change. (**a**) The electric motor starts; (**b**) the speed changes suddenly; (**c**) the load is suddenly applied.  
Figure 14 shows the comparison curves of pump outlet flow and Figure 15 is the partial magnification curve of pump outlet flow. It can be seen that whether it is a step rise, a step drop or a ramp in the flow rate, the overshoot and responsiveness of the pump outlet flow under the fuzzy PI control are significantly better than that of the traditional PI control. When the signal is a ramp signal, the two control methods can effectively follow the target control signal and the flow fluctuation in the response process is smaller. When the system enters a stable state, the pump outlet flow pulsation under the fuzzy PI control is smaller. When fuzzy PI control is used, the pump outlet flow overshoot is smaller, the response is faster, and the stability is better.  
Figure 14: The comparison curve of pump outlet flow.  
Figure 12: The output signal of the pilot handle.  
Figure 13: The displacement of the execute cylinder.  
Figure 16 is the cylinder speed curves and Figure 17 is the partial amplification curve of the cylinder speed. It can be seen from the partial amplification curve of the cylinder speed during shoveling that when the load is loaded during work, the cylinder speed fluctuates greatly, with large spikes and obvious jitter under the traditional PI control. While, under fuzzy PI control, the cylinder speed only fluctuates slightly, and the adjustment time is shorter. When the speed of the cylinder changes step by step, the cylinder speed has a large overshoot, the adjustment time is longer and the oscillation is obvious under the traditional PI control. While under the fuzzy PI control, cylinder speed is less overshoot, the adjustment time is shorter, and there is only a small oscillation. Therefore, when fuzzy PI control is used, the cylinder speed operation has better robustness and stability.  
Figure 16: The cylinder speed under two control system.  
Figure 15: The partial magnification curve of pump outlet flow. (**a**) Flow step rise; (**b**) flow stability; (**c**) flow step drop; (**d**) flow ramp response.  
From the simulation analysis, when the fuzzy PI control system is employed, the outlet flow impact of the hydraulic pump and the pulsation are smaller. The responsiveness and robustness are better than that of traditional PI control.