# Control Strategies for Piston Trajectory in Ionic Compressors for Hydrogen Storage
## 2 Methodology and Numerical Model
### Research Methodology  
In this paper, the design and research methodology of a piston speed control strategy for a hydrogen compressor based on valve control is shown in Figure 1. The entire research process can be divided into three phases: system design and calculation, numerical simulation, and an analysis of the results. The functional design of the hydraulically driven ionic compressor system and the proposition of the control scheme were carried out first in order to realize the speed control function of the hydraulic system and the gas compression function of the compressor. The structure of the compressor system is presented in Figure 2 and mainly comprises a gas valve, piston, gas compression cavity, electromagnetic directional valve, motor, pump, hydraulic cylinder, relief valve, and speed control component. An isolation chamber was designed in the compressor between the ionic liquid and the hydraulic oil. The leakage of either the ionic liquid or the hydraulic oil can be removed through the leakage channel when the piston moves down, connecting the isolation chamber and the leakage channel. A gas-liquid separator is required after the compressor as some ionic liquid droplets may be discharged with the hydrogen gas from the compressor.  
The speed control component is composed of a constant-differential-pressure-reducing valve and a throttle valve. The mass flow of the throttle valve can be controlled by changing the throttle valve opening as a constant difference between the pressure values at the two ends of the throttle valve can be guaranteed via the constant-differential-pressure-reducing valve. The piston trajectory is controlled by adjusting the flow of hydraulic oil in and out of the oil cylinder, using a speed component valve. Three control strategies, Position-P control, Position-S control, and Dual-PS control, are proposed in this paper, as shown in Figure 3. In Position-P control, the flow rate is regulated by adjusting the valve opening of the speed control element located at the inlet of the oil cylinder to match the hydraulic fluid flow to the flow rate required for the desired speed of movement of the piston. Position-S control regulates the piston speed by controlling the flow leaving the hydraulic cylinder through a speed-control component, which is similar in principle to Position-P control. Dual-PS control is the combination of Position-P control and Position-S control to achieve  
After finalizing the design of the structure of the compressor system, critical dimensions for the cylinders, pistons, valves, hydraulic cylinders, pumps, and hydraulic valves were determined based on the design requirements, as shown in Table 1. The designed inlet pressure was 12 MPa, which is an average value for the hydrogen production pressure [33], while the designed outlet pressure was 45 MPa, which is a typical value for hydrogen storage [34]. This means that pressure elevation is achieved through one-stage compression, with a pressure ratio of 3.75. The piston velocity equation used in the simulation is provided in Table 1[35]. The operating frequency of the piston was 5.0 Hz, and the motion velocity profile was set as a sinusoidal function. Additionally, the hydrogen flow rate was 200 \(\text{Nm}^{3}/\text{h}\), with an inlet temperature of 25 \({}^{\circ}\)C. After the key dimensions were obtained, a corresponding numerical simulation model of the entire system was established using AMESim. A numerical simulation was then conducted with the three control strategies. The results of an analysis of the control error, the internal energy produced, and the hydrogen mass delivered under the different control methods were obtained, based on which the optimal control approach for the entire system was identified.