Prop Solenoid $—$ Proportional solenoid as spool actuator with second-order dynamics

The Prop Solenoid component describes an actuator for a proportional valve with second-order spool dynamics and nonlinearities. It uses the same model for the actuator as the valve model Prop Valve.

The position of the spool is modeled as a second-order system with natural frequency ${\mathrm{\omega }}_{0}$, damping damp, limits for the velocity, and hysteresis for the position.

Input signal: $\mathrm{command}$ (of type Real)

Output signal: $\mathrm{position}$ (of type Real)

The steady state value of the position is given by:

 Command signal Steady state position $\mathrm{command}\le -1$ $\mathrm{position}=-1$ $-1<\mathrm{command}$ $<$ $1$ $-1<\mathrm{position}$ $<$ $1$ $1\le \mathrm{command}$ $\mathrm{position}=1$

This component accepts positive or negative input signals to give positive or negative positions. Typical solenoids displace their armature only in one direction, requiring two solenoids to build this kind of actuation system.

 Equations $\mathrm{mode}=\left\{\begin{array}{cc}\mathrm{Plus}& \left(\mathrm{pre}\left(\mathrm{mode}\right)=\mathrm{Plus}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{or}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{startpos}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}0<\mathrm{velocity}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{position}+\mathrm{hyst}\le \mathrm{posideal}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{position}\le 1\\ \left\{\begin{array}{cc}\mathrm{Minus}& \left(\mathrm{pre}\left(\mathrm{mode}\right)=\mathrm{Minus}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{or}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{startneg}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{velocity}<0\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{posideal}\le \mathrm{position}-\mathrm{hyst}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}-1\le \mathrm{position}\\ \mathrm{Null_}& \mathrm{otherwise}\end{array}\right\& \mathrm{otherwise}\end{array}\right\$ $\mathrm{startneg}=\left(\mathrm{pre}\left(\mathrm{mode}\right)=\mathrm{Null_}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{velocity}<0\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{posideal}\le \mathrm{position}-\mathrm{hyst}\right)$ $\mathrm{startpos}=\left(\mathrm{pre}\left(\mathrm{mode}\right)=\mathrm{Null_}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}0<\mathrm{velocity}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{and}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{position}+\mathrm{hyst}\le \mathrm{posideal}\right)$ $\mathrm{velocity}=\left\{\begin{array}{cc}{v}_{\mathrm{max}}& {v}_{\mathrm{max}}<\mathrm{velunlimited}\\ \left\{\begin{array}{cc}-{v}_{\mathrm{max}}& \mathrm{velunlimited}<-{v}_{\mathrm{max}}\\ \mathrm{velunlimited}& \mathrm{otherwise}\end{array}\right\& \mathrm{otherwise}\end{array}\right\$ ${\partial }_{t}\left(\mathrm{posideal}\right)=\mathrm{velocity}$ ${\partial }_{t}\left(\mathrm{position}\right)=\left\{\begin{array}{cc}0& \mathrm{mode}=\mathrm{Null_}\\ \mathrm{velocity}& \mathrm{otherwise}\end{array}\right\$ ${\partial }_{t}\left(\mathrm{velunlimited}\right)=\mathrm{command}{\mathrm{\omega }}_{0}^{2}-2\mathrm{damp}\mathrm{velunlimited}{\mathrm{\omega }}_{0}-\mathrm{posideal}{\mathrm{\omega }}_{0}^{2}$

Connections

 Name Description Modelica ID $\mathrm{position}$ Position of spool position $\mathrm{command}$ Commanded position of spool command

Parameters

 Name Default Units Description Modelica ID ${\mathrm{\omega }}_{0}$ $500$ $\frac{\mathrm{rad}}{s}$ Natural frequency of spool omega0 $\mathrm{damp}$ $\frac{7}{10}$ Damping coefficient of spool damp $\mathrm{hyst}$ $0.05$ Half of hysteresis width hyst ${v}_{\mathrm{max}}$ $25$ Max. spool velocity [1/s] vmax

Constants

 Name Value Units Description Modelica ID $\mathrm{Plus}$ $1$ Plus $\mathrm{Null}$ $0$ Null_ $\mathrm{Minus}$ $-1$ Minus