# Control Strategies for Piston Trajectory in Ionic Compressors for Hydrogen Storage
## 3 Results and Discussions  
### Results of Control Errors under Different Control Methods  
In order to obtain an optimal valve-controlled ionic compressor system with better performance, three control methods, Position-P control, Position-S control, and Dual-PS control, are compared in this paper. In this study, ten consecutive numerical simulations of the hydrogen compression cycle process were performed to ensure that the compressor reaches stable operation. The free piston of the ionic compressor is designed to move along a symmetric sinusoidal trajectory by means of speed control. The displacement curves of the free piston under different control methods are shown in Figure 6. It shows that the results were stabilized from the third cycle of operation. When the compressor undergoes expansion and suction, the displacement curve of the free piston controlled using Position-P control was found to be a straight line which deviated from the sinusoidal trajectory. However, the trajectory of the free piston controlled via Position-S control and Dual-PS control matched the sinusoidal trajectory. All three methods showed effective control in the compression and discharge processes as the piston trajectories aligned well with the sinusoidal trajectories. Although the maximum displacement of the free piston with the Position-P method was found to be the same as in the other two cases, a crash of the piston was found in this case. The displacement of the free piston at the bottom center position was found to be 6.64 \(\times\) 10\({}^{-4}\) m and 6.77 \(\times\) 10\({}^{-4}\) m when the system was controlled using the Position-P and Dual-PS methods, respectively. This study aimed to regulate the speed and trajectory of the piston by managing the flow rate in and out of the hydraulic cylinder via a speed control valve assembly. Figure 7 depicts the flow rate of the hydraulic oil into and out of the cylinders with the three control  
Figure 6: Displacement curves of the free piston in ten cycles under different control methods. methods during the sixth compression cycle. The hydraulic cylinder oil inlet curve showed a sinusoidal feature when the Position-P method was adopted, which was consistent with the design objective. However, in a time of 1.1-1.2 s, the hydraulic cylinder oil discharge of the Position-P control system increased rapidly and then stabilized at 250 L/min with the Position-P control method, which was inconsistent with the design. This was because the pressure of the hydraulic oil at its discharge port could not be quickly adjusted with the change in the gas compression chamber as the oil discharge port was directly connected to the oil tank through the reversing valve. Fluctuations in the oil flow rates at the inlet and outlet of the hydraulic cylinder were observed at around 1.0 and 1.1 s in all simulations with different control methods. These fluctuations were caused by the sudden change in the direction of the flow of hydraulic oil at 1.0 and 1.1 s due to the variation in the connecting location of the electromagnetic valve. Figure 8 shows the variation in the piston's motion speed with time for the three control methods. In comparing the speed curves of the various control methods with the set speed curves, it was evident that the sudden reversal of the direction due to the change in the electromagnetic valve caused the piston's speed to fluctuate to a certain extent due to hydraulic shock during reversal. The piston's speed was found to rise rapidly to 0.84 m/s and remained constant when the compressor entered the expansion and suction phases when the Position-P control method was used. This indicates a failure in the control of the piston's speed during the gas expansion and suction processes. Fluctuations in the velocity were found when the velocity was around 0 m/s. This is because when the connecting location of the reversing valve abruptly changed, the motion state of the hydraulic fluid in the connected piping underwent a significant alteration, causing a hydraulic shock.