# Cartridge Valve Actuator (IL)

Actuator that maintains equilibrium between valve and pilot pressures in an isothermal liquid system

**Library:**Simscape / Fluids / Valve Actuators & Forces

## Description

The Cartridge Valve Actuator (IL) block models an actuator that maintains equilibrium
between the valve and pilot-line pressures. The valve between ports
**A** and **B** remains closed until the pilot
spring **Spring preload force** is surpassed, at which point the piston
begins to move. The piston position is output as a physical signal at port
**S**. A schematic of a 4-port cqrtridge valve actuator is shown below.

### Actuator Force Balance

The actuator piston moves to adjust the pressure in the actuator chamber, which maintains equilibrium between the actuator port pressures and pilot line pressures:

$${p}_{A}{A}_{A}+{p}_{B}{A}_{B}={F}_{preload}+{F}_{pilot},$$

where:

*p*_{A}and*p*_{B}are the pressures at ports**A**and**B**.*A*_{X}is calculated from the**Port A to port X area ratio**.*A*_{B}is the port**B**area, $${A}_{X}-{A}_{A}$$, when the**Number of pressure ports**is set to`3`

. When the**Number of pressure ports**is set to`4`

,*A*_{B}is $${A}_{X}-{A}_{A}+{A}_{Y}$$.*F*_{preload}is the initial spring force in the system.*F*_{pilot}is $${p}_{X}{A}_{X}$$ if**Number of pressure ports**is set to`3`

and $${p}_{X}{A}_{X}+{p}_{Y}{A}_{Y}$$ if**Number of pressure ports**is set to`4`

.

### Piston Position

The steady piston displacement is calculated as:

$${x}_{steady}=\frac{F\epsilon}{k}=\frac{{F}_{A}+{F}_{B}-{F}_{pilot}-{F}_{preload}}{k}\epsilon ,$$

where *ε* is the **Opening
orientation**, which assigns movement in a positive direction
(extension) or negative direction (retraction). The dynamic change in piston
displacement is:

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

where *τ* is the **Actuator time
constant**. When $${\dot{x}}_{dyn}=\frac{{x}_{dyn}}{\tau}.$$ is less than the **Spring preload force**,
*x*_{steady} = 0.

If $${\dot{x}}_{dyn}=\frac{{x}_{dyn}}{\tau}.$$ is greater than the sum of the preload force and
*kx*_{stroke},
*x*_{steady} =
*x*_{stroke}.

### Opening Dynamics

If opening dynamics are modeled, a lag is introduced to the flow response to the
modeled control pressure. *p*_{control} becomes
the dynamic control pressure, *p*_{dyn};
otherwise, *p*_{control} is the steady-state
pressure. The instantaneous change in dynamic control pressure is calculated based
on the **Opening time constant**, *τ*:

$${\dot{p}}_{dyn}=\frac{{p}_{control}-{p}_{dyn}}{\tau}.$$

By default, **Opening dynamics** is set to
`Off`

.

### 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**. A smoothing function is applied to all calculated forces,
but primarily influences the simulation at the extremes of the piston motion.

The normalized force is calculated as:

$$\widehat{F}=\frac{{F}_{A}+{F}_{B}-{F}_{Preload}-{F}_{Pilot}}{k{x}_{stroke}}.$$

The **Smoothing factor**, *s*,
is applied to the normalized force:

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

### Assumptions and Limitations

Internal fluid volumes are not modeled in this block. There is no mass flow rate
through ports **A**, **B**,
**X**, and **Y**.

## Ports

### Conserving

### Output

## Parameters

## Version History

**Introduced in R2020a**