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Hydraulic double-acting servo cylinder with spring-centered plunger
The Double-Acting Servo Cylinder block models a hydraulic double-acting servo cylinder implemented as a spring-centered plunger.
Changing pressure at ports A and B shifts the spool from the neutral position in proportion to the pressure differential. Use the servo cylinder for control purposes.
The model of the cylinder uses the Double-Acting Hydraulic Cylinder (Simple), Translational Spring, Translational Damper, and Ideal Translational Motion Sensor blocks. The following figure shows the schematic diagram of the model.
The plunger is located initially in the middle of the stroke. The plunger displacement is computed with the following equations:
$$A\left({p}_{A}-{p}_{B}\right)=k\cdot x+B\cdot v+{F}_{HS}$$
$${F}_{HS}=\{\begin{array}{ll}\left(x-S/2\right)\cdot {K}_{p}\cdot v\hfill & \text{if}xS/2,v0\hfill \\ \left(x+S/2\right)\cdot {K}_{p}\cdot abs\left(v\right)\hfill & \text{if}x-S/2,v0\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}$$
where
p_{A},p_{B} | Pressures at port A and B, respectively |
A | Spool face area |
k | Spring rate |
B | Damping coefficient |
F_{HS} | Hard stop force |
K_{p} | Stop penetration coefficient |
S | Piston stroke |
v | Piston velocity |
x | Piston displacement |
Connection P is a physical signal output port that outputs the plunger displacement from the central position. Connections A and B are hydraulic conserving ports. Pressure at port A moves the plunger in the positive direction.
Friction between moving parts is not taken into account.
Inertia effects are not taken into account.
Fluid compressibility is not taken into account.
Leakage flows are assumed to be negligible.
The hard stops are assumed to be fully inelastic. For details, see the Double-Acting Hydraulic Cylinder (Simple) block reference page.
The face area of the piston. The default value is 1e-4 m^2.
The full piston stroke, from one hard stop to another. The piston is located initially in the middle of the stroke and can travel half a stroke in the positive and negative direction. The default value is 0.005 m.
The spring rate of the centering springs. The default value is 1000 N/m.
The damping coefficient in the contact between the piston and the case. The default value is 150 N/(m/s).
The penetration property of the piston hard stop. The hard stop is represented as absolutely inelastic, and the property is characterized by the penetration coefficient. The default value of the coefficient is 1e12 N/m/(m/s).