## 3 Case Studies
### Results and Discussion
#### 3.2.2 Step Responses to Loads  
After the experiments in step responses to reference inputs, step responses to loads under different and equal vales of \(K_{vp}\) are carried out, as shown in Figures 9 and 10. Experimental condition are as follows: initial pump voltage \(u_{p0}=8.6\) V, initial valve voltage \(u_{v0}=-2.8\) V and PI parameters of the control circuit are set as in Table 2. The reference speed of the hydraulic motor is set to \(60\) r/min, pressure disturbance is generated by the PRV and the high-pressure side of the system produces step pressures from \(4\) MPa to \(6\) MPa and \(6\) MPa to \(4\) MPa.  
The following conclusions can be made:  
(1) The response speed to load disturbance in the LVPC is faster than that in single pump control and in valve control. That is because \(K_{sl}\) determines response speed and \(K_{sl}>K_{sv}\)_or_\(K_{sl}>K_{sp}\) is always true in the experiment.  
(2) The velocity stiffness to load disturbance in the LVPC is lower than that in single pump control. Because velocity stiffness is inversely proportional to the leakage coefficients, after adding the valve control to V-PC systems, the total leakage coefficient of LVPC systems increase significantly and  
Figure 9: Step response to loads under different weight ratios \(K_{vp}\). (**a**) Motor speed response; (**b**) Pump and valve voltage variation; (**c**) System pressure and flow response.  
the difficulty of parameter prediction. The LVPC system also has lower velocity stiffness, as velocity stiffness is inversely proportional to leakage coefficients.  
(2) The role of valve control and pump control in the LVPC system can be adjusted by changing the valve-pump weight ratio, which determines the flow distributions between the valve and the pump.  
(3) In the LVPC system, the valve control and the pump control work together on the hydraulic motor. As long as the weight factors are set properly, LVPC will have a greater open-loop gain than VSPC and a faster response speed. However, it should be noted that if the weight is set too large, the system may respond too quickly and there will be a large overshoot.  
(4) It is well known that pump control efficiency is high and valve control efficiency is low because of throttling losses. LVPC is a composite control of valve control and pump control and the greater the valve-pump weight ratio, the greater the valve control effect, the lower the system efficiency. Therefore, in order to make the system have higher response while keeping high efficiency, the valve-pump weight ratio should be reasonably set, so that the pump provides a larger flow rate and the valve only works in a small flow state.  
[PERSON] and [PERSON] conceived and designed the experiments; [PERSON] performed the experiments; [PERSON] collected and analyzed the data; [PERSON] and [PERSON] contributed materials/analysis tools; [PERSON] and [PERSON] wrote the paper.  
This work is supported by a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions and the Fundamental Research Funds for the Central Universities (No. 2015 QNA33).  
The authors declare no conflict of interest.