# Analysis and Suppression of Self-Excited Oscillations in Pressure Servo Valve System
## 3 Pressure Oscillation Mechanism Analysis  
PSVS shows the periodic oscillation in simulation and experiment. However, PSVS has neither an excitation source nor a resonance component and structural parameters that change periodically. However, there is a large number of feedback and regulation loops inside the system. Therefore, according to the mechanism of oscillation induction, the pressure oscillation is most likely to be self-excited oscillation, which is very common in nonlinear systems.  
If self-excited oscillation occurs in a nonlinear system, an essential nonlinear factor exists in the system consequently. The principle of pressure servo valve power stage is shown below.  
The pressure servo valve inevitably overshoots its output pressure under the action of step signaling. The overshoot pressure (which is higher than expected output pressure) will disrupt the dynamic force balance of the main spool, and the main valve spool will generating negative displacement (\(x_{\varphi}<0\)). At this time, port B in Figure 10 will connect to port H. Additionally, due to the differential pressure, the oil that comes from the cylinder will flow into the oil return cavity through the power stage spool window. This oil will be divided into two paths. The oil that goes along path 1 will enter the closed cavity (which is shown in Figure 10), causing a sudden pressure increase in the cavity. The oil that goes along path 2 will enter the oil return cavity (formed by the hose between the pressure servo valve and relief valve), causing a sudden pressure increase in said cavity. To further illustrate the pressure dynamics in the oil return cavity, a model is built, as shown in Figure 11.  
Figure 11: Model of the oil return cavity.  
Figure 10: Pressure servo valve power stage.  
The relationship between the pressure gradient and the flow is as follows  
\[\dot{p}_{h}=\frac{\beta}{V_{h}}(Q_{in}-Q_{out}) \tag{15}\]  
For the relief valve, there is an approximately linear relationship between the output flow and the pressure \(p_{h}\).  
\[Q_{out}=k_{j}p_{h} \tag{16}\]  
Therefore, the following formula can be obtained.  
\[\dot{p}_{h}=\frac{Q_{in}}{k_{j}}\left(1-e^{-\frac{\beta_{j}}{V_{h}}t}\right) \tag{17}\]  
From the above formula, it can be seen that  
(1) The volume of the oil return cavity \(V_{h}\) determines the time constant. The smaller \(V_{h}\) is, the faster the backpressure changes.  
(2) The input flow \(Q_{in}\) determines the amplitude of the dynamic backpressure. The larger \(Q_{in}\) is, the farther the backpressure deviates from the set value of 0.6 MPa. Therefore, the larger the negative \(x_{v}\) is, the more obvious the backpressure \(p_{h}\) changes.  
The sudden change of backpressure will cause the resultant force (along the negative direction, \(x_{v}<0\)) which acts on the main valve spool increases furtherly. In addition, the positive feedback will form to force the main valve spool to move to the right side, until the output pressure drops more to form a new force balance state. This process can be represented by the control block diagram shown in the Figure 12.  
According to the definition given by physicist [PERSON], a self-excited oscillation system is a closed-loop system consisting of a main oscillation subject, an energy source, a controller and a feedback unit, which is shown in Figure 13.  
In PSVS, the buildup pressure \(p_{c}\) in Figure 10 is the energy source, the main valve spool is the main oscillation subject, and the positive feedback formed by the backpressure  
Figure 12: Pressure servo valve power stage feedback control block diagram.  
Figure 13: Self-excited oscillation feedback mechanism.  
is the internal feedback information to maintain the energy replenishment. Therefore, the structure of power stage meets the structural characteristics of self-excited oscillation system. Therefore, the pressure oscillation of the PSVS is the self-excited oscillation caused by backpressure positive feedback.