# Analysis and Suppression of Self-Excited Oscillations in Pressure Servo Valve System
## 4 Oscillation Suppression of PSVS
### Verification of Oscillation Suppression Method
#### 4.2.2 Stability Margin Analysis
\[\widetilde{T}_{r}=K_{fg}(r\widetilde{\psi}+\widetilde{x}_{c})(r+b) \tag{28}\]6  
\[\widetilde{T}_{r}=K_{fg}(r\widetilde{\psi}+\widetilde{x}_{c})(r+b) \tag{28}\]7  
The control block diagram from the power stage spool displacement \(x_{v}\) to the output pressure \(p_{b}\) can be obtained as shown in \[\widetilde{T}_{r}=K_{fg}(r\widetilde{\psi}+\widetilde{x}_{c})(r+b) \tag{28}\]8  
As can be seen from Figure 23, the PSVS is a typical closed-loop control system, and there are complex cross-feedback loops and feedforward loops. Therefore, it is extremely difficult to solve the system open-loop transfer function directly. To solve the stability margin of the PSVS, this paper divides the system into two parts and makes reasonable simplification to establish their respective transfer function models, namely, the pre-stage  
\[\widetilde{T}_{r}=K_{fg}(r\widetilde{\psi}+\widetilde{x}_{c})(r+b) \tag{28}\]9 Block diagram of PSVS. \[k_{q}\widetilde{x}_{s}-k_{c}\widetilde{p}_{c}=A_{c}s\widetilde{x}_{c}+A_{\
u}s \widetilde{x}_{\
u}+\frac{V_{cv}}{\beta}s\widetilde{p}_{c} \tag{29}\]0 Control block diagram from main valve spool displacement to output pressure. stability transfer function model and the power stage transfer function model. When judging the stability of the system, both parts are taken into consideration. (1) Pre-stage stability margin analysis. In this paper, the pressure servo valve pre-stage includes two parts: jet amplifier and feedback stage, where the structure is shown in Figure 24a. Its working principle is similar to that of the force feedback two-stage hydraulic servo valve, as shown in Figure 24b. Therefore, the pressure servo valve pre-stage transfer function can be established with reference to the jet pipe force feedback two-stage hydraulic servo valve. The control block diagram of pre-stage is shown in \[k_{q}\widetilde{x}_{s}-k_{c}\widetilde{p}_{c}=A_{c}s\widetilde{x}_{c}+A_{\
u}s \widetilde{x}_{\
u}+\frac{V_{cv}}{\beta}s\widetilde{p}_{c} \tag{29}\]1 It can be seen that when establishing the feedback valve spool force balance equation, the force of the feedback rod is ignored because the spring stiffness at both ends of the feedback valve spool is much larger than the feedback rod stiffness. After ignoring some factors that have little influence, such as \(p_{h}\) (because \(p_{c}\gg p_{h}\)), the transfer function (from the displacement of jet pipe \(x_{s}\) to the displacement of feedback valve spool \(x_{c}\)) can be obtained below. \[k_{q}\widetilde{x}_{s}-k_{c}\widetilde{p}_{c}=A_{c}s\widetilde{x}_{c}+A_{\
u}s \widetilde{x}_{\
u}+\frac{V_{cv}}{\beta}s\widetilde{p}_{c} \tag{29}\]2  
The pressure servo valve pre-stage Bode diagram is shown in \[k_{q}\widetilde{x}_{s}-k_{c}\widetilde{p}_{c}=A_{c}s\widetilde{x}_{c}+A_{\
u}s \widetilde{x}_{\
u}+\frac{V_{cv}}{\beta}s\widetilde{p}_{c} \tag{29}\]3  
\[k_{q}\widetilde{x}_{s}-k_{c}\widetilde{p}_{c}=A_{c}s\widetilde{x}_{c}+A_{\
u}s \widetilde{x}_{\
u}+\frac{V_{cv}}{\beta}s\widetilde{p}_{c} \tag{29}\]4 Servo valve force feedback structure: (**a**) Pressure servo valve pre-stage, (**b**) Jet pipe force feedback two-stage hydraulic servo valve. \[k_{q}\widetilde{x}_{s}-k_{c}\widetilde{p}_{c}=A_{c}s\widetilde{x}_{c}+A_{\
u}s \widetilde{x}_{\
u}+\frac{V_{cv}}{\beta}s\widetilde{p}_{c} \tag{29}\]5 Block diagram of pressure servo valve pre-stage. It can be seen that the pressure servo valve pre-stage has a large amplitude margin (12.1 dB > 6 dB) and phase angle margin (84.3 deg > 30 deg), which can maintain stability under certain external disturbances. (2) Pressure servo valve power stage stability margin analysis. The control block diagram from buildup pressure \(p_{c}\) to output pressure \(p_{b}\) is as shown in \[k_{q}\widetilde{x}_{s}-k_{c}\widetilde{p}_{c}=A_{c}s\widetilde{x}_{c}+A_{\
u}s \widetilde{x}_{\
u}+\frac{V_{cv}}{\beta}s\widetilde{p}_{c} \tag{29}\]6  
The load differential pressure takes different values in the case of \(x_{p}>0\) and \(x_{v}<0\). From the analysis in subSection 4.2.1, it can be obtained that \(p_{b}\approx 9.5\) MPa.