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This example shows a solenoid with a spring return. The solenoid is modeled as an inductance whose value L depends on the plunger position x. The back emf for a time-varying inductance is given by:

$v=L{di\over dt}+i{dL\over dt}\quad\quad\quad(1)$

As L depends on x, this becomes:

$v=L{di\over dt}+i{dL\over dx}{dx\over dt}\quad\quad(2)$

${dL\over dx}$ can be derived from manufacturer force-stroke data using the relationship:

$force = 0.5*i^2{dL\over dx}\quad(3)$

${dL\over dx}$ can then be integrated to get L as a function of x.

In the model, equation 2 is rearranged to solve for i, and then implemented using Physical Signal blocks. A controlled current source then constrains the current to equate to i.


Solenoid Subsystem

Simulation Results from Simscape Logging

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