## 3 Case Studies  
### Experiment  
An experimental LVPC system based on the principle of Figure 1 is set up as shown in Figure 4 and its main configuration as listed in Table 1. The rated pressure of the system is 25 MPa, flow 35 L/min, maximum speed of the hydraulic motor 90 r/min. The flushing device includes a hydraulically controlled directional control valve and a relief valve. A portion of the hot oil from the motor low pressure side flows out of the device to cool the system. The pressure of the relief valve is called the flushing pressure and is generally lower than the replenishing pressure by 0.2-0.3 MPa. Here it is set to 0.5 MPa. In Figure 4, the left is a driving motor and the right is a loading pump, they have the same displacement and the loading pressure is regulated by a proportional relief valve. The rotary inertia block is installed between the two hydraulic motors, its total weight being 900 kg and its total inertia 72 kg\(\cdot\)m\({}^{2}\). In order to study dynamic response under different inertias, the inertia block is designed to be modular, with one basic and four small blocks.  
A virtual control system is developed using the LabVIEW platform as shown in Figure 5. The system pressures, pump flow rates, valve flow and hydraulic motor's rotary speed are measured by corresponding sensors and are fed back to an industrial computer via a data acquisition card. After data processing, the control system outputs control signals to the inverter, PTV and PRV. The control system integrates the functions of data acquisition, control, display and data storage and can work under LVPC and VSPC modes.  
From Section 2.2, we know that the valve-pump parallel system is a type-0 system and is unstable before compensation, so the PI compensation is applied to the pump control circuit and valve control circuit. The PI transfer function is  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Components** & **Specification** \\ \hline Electric motor & power:7.5 Kw; rated speed:3000 r/min; control voltage: 0–10 V \\ Inverter & power:11 kW with vector control; frequency range:0.1–100 Hz; \\ Fixed pump & displacement:12.6 mL/r; speed range:500–3000 r/min \\ Hydraulic motor & speed range: 0–90 r/min; displacement:468 mL/r; rated pressure: 40 MPa \\ PTV & rate flow: 9 L/min at 1.5 MPa per notch; frequency: 60 Hz; damping ratio: 0.7 \\ Proportional relief valve & pressure range: 0.7–31.5 MPa; rate flow:200 L/min \\ Rotary inertia & 72 kg\(\cdot\)m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: System configuration.  
Figure 4: Experimental system. (**a**) A view of the experimental system; (**b**) Loading system.  
Figure 5: Measurement and control system. (**a**) Control principle; (**b**) Interface.  
\[G_{c}=K_{p}\bigg{(}1+\frac{1}{T_{i}s}\bigg{)}=K_{p}+\frac{K_{I}}{s} \tag{16}\]  
where \(K_{p}\) is the proportional gain, \(T_{i}\) is the internal time, \(K_{I}\) is the internal gain and \(K_{I}=K_{p}/T_{i}\). Thus \(K_{I}\) is defined by \(K_{p}\) and \(T_{i}\).  
Step response experiments of the valve control and the pump control circuits are carried out as shown in Figure 6, and optimal PI parameters are obtained through repeated experiments, as shown in Table 2. A relationship, \(K_{I}\gg K_{p}\) is maintained in the two control circuits, so PI compensation can be considered as an internal compensation mechanism, as discussed in Section 2.2.4. The experimental results show that the selected PI parameters are reasonable and the valve control responds faster than the pump control.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Control Mode** & \(K_{p}\) & \(T_{i}\) & \(K_{I}\) \\ \hline Pump control & 0.3 & 0.18 & 1.67 \\ Valve control & 0.6 & 0.12 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Coefficients of PI under different mode.  
Figure 6: Step response of pump control and valve control. (**a**) Pump control circuit; (**b**) Valve control circuit.