[Scilab-users] Modeling current in a solenoid

[Michael Greenish]

Hi Tim,
Thank you for the quick feedback.  The inductance changes with position and I have taken measurements of the inductance vs. position.  I have the position data from model of the mechanical system, a simply sprung-damped mass system.  
What I don't know how to do is to either break up the math into constituent blocks (I can't find a block for Euler number or to program a block that can take the inductance in as an input parameter (although I do program in various languages, I've never programmed in scilab or xcos before).  
What would be the best way to proceed, in your opinion? Separate blocks or program a custom block?
Thanks,
Mike

      From: Tim Wescott <tim at wescottdesign.com>
 To: Michael Greenish <greanie at yahoo.com>; Users mailing list for Scilab <users at lists.scilab.org> 
 Sent: Monday, September 21, 2015 8:55 PM
 Subject: Re: [Scilab-users] Modeling current in a solenoid
   
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




  
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