# Analysis and Suppression of Self-Excited Oscillations in Pressure Servo Valve System
## 4 Oscillation Suppression of PSVS  
### Oscillation Suppression Method  
As described in the previous section, when \(x_{v}<0\), the oil from the cylinder enters the closed cavity which is shown in Figure 14. Since the closed cavity has only one flow path, the cavity is very sensitive to the changes in flow; that means even small changes in flow can cause dramatic pressure oscillation in that cavity. Additionally, it will triggering a backpressure positive feedback on the main spool valve.  
Therefore, in order to reduce the backpressure positive feedback effect of the main spool, two structure optimization methods are taken. First, the closed cavity is connected to the cavity at the left end of the feedback valve spool to transform the closed cavity into an open cavity. Therefore, the volume of the cavity increases, and the sensitivity of the cavity to the flow gradient is reduced. Secondly, a damping hole is added between the backpressure feedback channel and Prot H to achieve the attenuation of the backpressure oscillation, so that the pressure in front of the backpressure feedback channel tends to be smooth. The principle of the structure-optimized servo valve is shown in Figure 15.  
Figure 14: Pressure servo valve structure.  
To illustrate the attenuation effect of damping holes on backpressure oscillations, a simulation model of pressure oscillations with damping holes is established in the Amesim software, as shown in Figure 16.  
The parameters in the simulation model are as same as those in Table 2. The orifice parameters are shown in Table 4.  
When the pressure source signal is \(p=9.5+0.5\sin(2\pi\times 25t)\), the input pressure and the pressure in the h  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Diameter** & **Length** & **Diameter of Inlet Runner** & **Model** \\ \hline Thin-walled & 1 mm & – & 2 mm & \(\xi=f\left(\text{Re},\frac{A_{c}}{A_{1}}\right)\) \\ Thick-walled & 1 mm & 10 mm & 2 mm & \(\xi=f\left(\text{Re},\frac{A_{c}}{A_{1}};\frac{1}{D_{h}}\right)\) \\ \hline \end{tabular}
\end{table}
Table 4: Office parameters.  
Figure 16: Simulation model of pressure oscillation with damped orifice.  
Figure 15: Principle of structure-optimized pressure servo valve.  
It can be seen that the sinusoidal pressure oscillation from the pressure source is greatly attenuated after passing through the orifice: the peak-to-peak value drops from 10 MPa to 0.3 MPa. Moreover, it is observed that the attenuation of pressure oscillations by the thin-walled orifice is better than that by the thick-walled orifice.  
Therefore, it can be said that the pressure in the backpressure feedback channel can be approximated as a constant value (\(p_{h}=0.6\) MPa) after passing through the orifice. At this time, the dynamic model of the PSVS is as follows.  
\[T_{d}=K_{t}\Delta i+K_{m}\psi \tag{18}\]  
\[T_{d}=J_{a}\frac{\mathrm{d}^{2}\psi}{\mathrm{d}t^{2}}+B_{a}\frac{\mathrm{d} \psi}{\mathrm{d}t}+K_{a}\psi+T_{r} \tag{19}\]  
\[T_{r}=K_{fg}(r\psi+x_{c})r \tag{20}\]  
\[k_{q}x_{s}-k_{c}p_{c}=A_{c}\frac{\mathrm{d}x_{c}}{\mathrm{d}t}+A_{v}\frac{ \mathrm{d}x_{v}}{\mathrm{d}t}+\frac{V_{cv}}{\beta}\frac{\mathrm{d}p_{c}}{ \mathrm{d}t} \tag{21}\]  
\[(p_{c}-p_{h})A_{c}-K_{fg}(r\psi+x_{c})-2K_{c}x_{c}=m_{c}\tilde{x}_{c}+B_{c} \dot{x}_{c} \tag{22}\]  
\[p_{c}A_{v}-p_{b}A_{b}-0.6A_{h}=M_{v}\tilde{x}_{v}+B_{v}\dot{x}_{v}+\Big{(}K+K _{f}\Big{)}x_{v}+Kx_{v0} \tag{23}\]  
\[Q_{L}=C_{d}Wx_{v}\sqrt{\frac{2}{\rho}\bigg{(}\frac{1+sign(x_{v})}{2}p_{s}+ \frac{-1+sign(x_{v})}{2}p_{b}-sign(x_{v})p_{h}\bigg{)}} \tag{24}\]  
\[Q_{L}-C_{b}p_{b}=A_{g}\frac{\mathrm{d}\psi}{\mathrm{d}t}+\frac{V_{g}+V_{b}}{ \beta}\frac{\mathrm{d}p_{b}}{\mathrm{d}t} \tag{25}\]  
Figure 17: Pressure in the hose under the action of the sinusoidal pressure source: (**a**) pressure source; (**b**) pressure in hose (after thin-walled orifice); (**c**) pressure in hose (after thick-walled orifice); (**d**) pressure in hose (without orifice).  
\[A_{g}p_{b}=M_{g}\frac{\mathrm{d}^{2}y}{\mathrm{d}t^{2}}+B_{g}\frac{\mathrm{d}y}{ \mathrm{d}t}+K_{g}y \tag{26}\]