Pilot Valve Actuator (IL)

Single-acting or double-acting actuator controlled by a pilot pressure in an isothermal liquid network

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Description

The Pilot Valve Actuator (IL) block models a single-acting or double-acting actuator controlled by a pilot pressure for control of a connected valve or orifice in an isothermal liquid network.

For the single-acting actuator, when the control pressure, P_X – P_atm, exceeds the Spring preload force at port X, the piston begins to actuate in the direction assigned by the Mechanical orientation parameter.

For the double-acting actuator, the control pressure P_control is the difference between P_X – P_atm and P_Y – P_atm. The piston actuates in the direction of the larger applied pressure differential, opposing the spring force at the opposite port. When the piston motion reverses, this spring does not extend and does not exert a counterbalancing force on the piston position.

The pistons at port X and port Y are attached to a single spool. Both springs restore the spool to its neutral position when F_spool falls below the opposing spring preload force. For single-acting actuators, the neutral position is at port X. For double-acting actuators, the neutral position is at the center of the actuator.

Single-Acting Actuator

The force on the piston is created by the pressure differential between port X and atmospheric pressure:

$$F_{spool}=\left(p_X-p_{atm}\right)A_X,$$

where A_X is the Piston area at port X. When F_spool is greater than the Spring preload force at port X, the piston begins to move.

Schematic of a Single-Acting Actuator

Piston Displacement

The instantaneous piston displacement is calculated as:

$${\dot{x}}_{dyn}=\frac{x_{steady}-x_{dyn}}{\tau },$$

where the steady piston position, x_steady, is the piston position at the current pressure differential, proportional to the spring force at maximum piston stroke:

$$x_{steady}=F{x}_{stroke}\epsilon =\frac{F_{spool}-F_{pre}}{F_{\max }-F_{pre}}{x}_{stroke}\epsilon ,$$

where:

• F_pre is the Spring preload force at port X.

• F_max is the maximum spring force acting against piston displacement, $$F_{\max }=K{x}_{stroke}+F_{pre},$$ and where K is the Spring stiffness at port X.

• x_stroke is the Piston stroke from port X.

• ε is the Mechanical orientation, which indicates piston movement in a positive direction (extension) or negative direction (retraction).

If the force on the piston is less than the Spring preload force at X, the piston remains at the neutral position or moves to the neutral position. If the force on the piston meets or exceeds the maximum spring force, the piston remains at the stroke until the applied pressure changes.

Double-Acting Actuator

The difference between the forces at ports X and Y dictates the piston motion:

$$F_{spool}=\left(p_X-p_{atm}\right)A_X-\left(p_Y-p_{atm}\right)A_Y.$$

The pressure applied at port X shifts the spool away from the chamber at X and opposes the spring at port Y. Similarly, the pressure applied at port Y shifts the spool away from the chamber at Y and opposes the spring at port X. When the spool reverses direction, the formerly extended spring compresses, exerting a force on the spool. The formerly compressed spring, the spring at the port in the direction of motion, does not extend and does not influence the spool position.

Schematic of a Double-Acting Actuator

Piston Displacement

The piston displacement is calculated as:

$${\dot{x}}_{dyn}=\frac{x_{steady}-x_{dyn}}{\tau },$$

where the steady piston position, x_steady, is the piston position at the current pressure differential, proportional to the spring force at maximum piston stroke:

$$x_{steady}=\left(F_Y{x}_{stroke,Y}-F_X{x}_{stroke,X}\right)\epsilon =\left(\frac{F_{spool}-F_{pre,Y}}{F_{\max ,Y}-F_{pre,Y}}{x}_{stroke,Y}-\frac{\left(-F_{spool}-F_{pre,X}\right)}{F_{\max ,X}-F_{pre,X}}{x}_{stroke,X}\right)\epsilon ,$$

where:

• F_pre,X and F_pre,Y are the Spring preload force at port X and Spring preload force at port Y, respectively.

• F_max,X and F_max,Y are the maximum spring forces acting against piston displacement at ports X and Y, respectively, where:

  $$F_{\max }=K{x}_{stroke}+F_{pre},$$

  K is the spring stiffness per port.

• x_stroke is the piston stroke per port.

• ε is the Mechanical orientation, which assigns the signal for piston movement as positive (extension) or negative (retraction).

If the force on the piston is less than the respective port spring preload force, the piston remains or returns to the neutral position. If the force on the piston meets or exceeds the maximum spring force for the respective port, the piston remains at the piston stroke until the applied pressure changes.

Numerically-Smoothed Force

When the actuator is close to full extension or full retraction, you can maintain numerical robustness in your simulation by adjusting the block Smoothing factor. With a nonzero smoothing factor, a smoothing function is applied to all calculated forces, but primarily influences the simulation at the extremes of the piston motion.

When Actuator configuration is set to Single-acting, the normalized force on the piston is calculated as:

$${\widehat{F}}_X=\frac{F_{spool}-F_{Pre}}{F_{\max }-F_{Pre}}.$$

When Actuator configuration is set to Double-acting, the normalized force on the piston at X is calculated as:

$${\widehat{F}}_X=\frac{-F_{spool}-F_{Pre,X}}{F_{\max ,X}-F_{Pre,X}}.$$

and the normalized force at Y is calculated as:

$${\widehat{F}}_Y=\frac{F_{spool}-F_{Pre,Y}}{F_{\max ,Y}-F_{Pre,Y}}.$$

When the Smoothing factor, s, is nonzero, each normalized force incorporates smoothing:

$${\widehat{F}}_{X,smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\widehat{F}}_X^2+{\left(\frac{s}{4}\right)}^2}-\frac{1}{2}\sqrt{{\left({\widehat{F}}_X-1\right)}^2+{\left(\frac{s}{4}\right)}^2},$$

$${\widehat{F}}_{Y,smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\widehat{F}}_Y^2+{\left(\frac{s}{4}\right)}^2}-\frac{1}{2}\sqrt{{\left({\widehat{F}}_Y-1\right)}^2+{\left(\frac{s}{4}\right)}^2}.$$

Ports

Conserving

X — Pressure port P_X

isothermal liquid

Pressure at port X. There is no mass flow through the port.

Y — Pressure port P_Y

isothermal liquid

Pressure at port Y. There is no mass flow through the port.

Dependencies

To enable this port, set Actuator type to Double-acting.

Output

S — Piston displacement, m

physical signal

Piston displacement, specified as a physical signal. The displacement sign corresponds to the direction specified in the Mechanical orientation parameter.

Parameters

Actuator configuration — Type of actuator modeled

Single-acting (default) | Double-acting

Type of actuator modeled.

Piston area at port X — Cross-sectional area of piston rod at port X

1e-4 m^2 (default) | positive scalar

Cross-sectional area of the piston rod at port X.

Piston area at port Y — Cross-sectional area of piston rod at port Y

1e-4 m^2 (default) | positive scalar

Cross-sectional area of the piston rod at port Y.

Dependencies

To enable this parameter, set Actuator type to Double-acting.

Spring preload force — Force in the neutral position

20 N (default) | scalar

Force acting against the piston in the neutral position.

Dependencies

To enable this parameter, set Actuator type to Single-acting.

Spring preload force at port X — Force at port X in the neutral position

20 N (default) | scalar

Force at port X in the neutral position.

Dependencies

To enable this parameter, set Actuator type to Double-acting.

Spring preload force at port Y — Force at port Y in the neutral position

20 N (default) | scalar

Force at port Y in the neutral position.

Dependencies

To enable this parameter, set Actuator type to Double-acting.

Spring stiffness — Stiffness coefficient

15e3 N/m (default) | positive scalar

Spring stiffness factor. The maximum spring force is determined from the stiffness, K, and the Spring preload force: $$F_{\max }=K{x}_{stroke}+F_{pre},$$

Dependencies

To enable this parameter, set Actuator type to Single-acting.

Spring stiffness at port X — Stiffness coefficient at port X

15e3 N/m (default) | positive scalar

Port X spring stiffness. The maximum spring force is determined from the stiffness, K, and the Spring preload force at port X: $$F_{\max }=K{x}_{stroke}+F_{pre},$$

Dependencies

To enable this parameter, set Actuator type to Double-acting.

Spring stiffness at port Y — Stiffness coefficient at port Y

15e3 N/m (default) | positive scalar

Port Y spring stiffness. The maximum spring force is determined from the stiffness, K, and the Spring preload force at port Y: $$F_{\max }=K{x}_{stroke}+F_{pre},$$

Dependencies

To enable this parameter, set Actuator type to Double-acting.

Piston stroke — Maximum piston travel distance

5e-3 m (default) | positive scalar

Maximum piston travel distance.

Dependencies

To enable this parameter, set Actuator type to Single-acting.

Piston stroke from port X — Maximum piston travel distance at port X

5e-3 m (default) | positive scalar

Maximum piston travel distance at port X.

Dependencies

To enable this parameter, set Actuator type to Double-acting.

Piston stroke from port Y — Maximum piston travel distance at port Y

5e-3 m (default) | positive scalar

Maximum piston travel distance at port Y.

Dependencies

To enable this parameter, set Actuator type to Double-acting.

Smoothing factor — Numerical smoothing factor

0.01 (default) | positive scalar in the range [0,1]

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

Actuator dynamics — Whether to account for transients during actuation

Off (default) | On

Whether to account for transient effects in the spool position due to actuation. Setting Actuator dynamics to On approximates actuator motion by introducing a first-order lag in the spool position. The Actuator time constant also impacts the modeled dynamics.

Actuator time constant — Piston displacement time constant

0.1 s (default) | positive scalar

Constant that captures the time required for the piston to reach steady-state when moving from one position to another. This parameter impacts the modeled actuator dynamics.

Dependencies

To enable this parameter, set Actuator dynamics to On.

Mechanical orientation — Piston displacement direction

Pilot pressure at port X causes positive piston displacement (default) | Pilot pressure at port X causes negative piston displacement

Sets the piston displacement direction based on the configuration at port X. If Actuator configuration is set to Double-acting, the displacement force at port Y acts in the opposite direction of the force at port X. Pilot pressure at port X causes positive piston displacement corresponds to positive displacement when the pressure at X pushes the piston towards port Y. Pilot pressure at port X causes negative piston displacement corresponds to negative displacement when the pressure at X pushes the piston towards port Y.

Model Examples

Hydraulic Axial-Piston Pump with Load-Sensing and Pressure-Limiting Control

A test rig designed to investigate the interaction between an axial-piston pump and a typical control unit simultaneously performing the load-sensing and pressure-limiting functions. To increase the fidelity of the simulation, this example uses a detailed model of the pump that accounts for the interaction between the pistons, swash plate, and valve plate.