[Scilab-users] Modeling current in a solenoid

[Tim Wescott]

On Mon, 2015-09-21 at 08:00 +0000, Michael Greenish wrote:
> Hi,
> 
> 
> I need to model the current in a solenoid.  I would use a resistor
> with the standard inductor model but the inductance changes
> considerably with position of the solenoid plunger (as the solenoid is
> closing).  The standard inductor model only accommodates a fixed
> inductance.
> 
> 
> The equation for inductor current is:
> 
> 
>       I(t) = (V/R)[1-eˆ(-Rt/L)]
> 
> 
> Anyone have any suggestions?
> 
Hey Mike:

That's the equation for inductor current when driven by a voltage, yes.
It comes from the differential equation:

i(t) * R + (d/dt i(t)) L = V.  It's a first-order ordinary linear
differential equation.

Life gets complicated when you have that solenoid in there.  I'm almost
certain that the correct way to model the i/v behavior of the solenoid
is

v_l(t) = d/dt (i(t) * L(t))

-- in other words, accept that both current and inductance change with
time, and take the derivative of the pair.  The place to look to check
up on my assumption is texts in electrical machines (it's a 3rd-year
electronics course.  My book is "Electric Machines: Steady-State Theory
and Dynamic Performance" by Mulukutla S. Sarma, WCB, 1985.

Note that, at best, you'll have to treat the system as a time-varying
linear system, and you may have to treat the system as being nonlinear
(depending on how quickly the solenoid position varies with time
compared to the current).  You'll also see that finding the inductance
vs. position relationship is (ehem) left as an exercise to the reader.

This isn't a complete answer, but I hope that it sets your feet on the
right road.

-- 

Tim Wescott
www.wescottdesign.com
Control & Communications systems, circuit & software design.
Phone: 503.631.7815
Cell:  503.349.8432