Solving Current Regulation on Motor-Driven Wagon

[ponjavic]

Hi, I'm trying to do current regulation on a motor driven wagon running on a track.
Instead of having a closed loop servo where the feedback is the speed or position the regulation is to use current. I'm struggling a bit with the theory.

This is what I'm used to doing:
http://www.engin.umich.edu/group/ctm/examples/motor/motor.html
Look at 1. Transfer function.
Now, Newton's law in this system is a 2nd order differential equation which can be solved.
I thought that I need a transfer function I/V which I was able to obtain:

I(s)                Js + b
-----  = -----------------------
  V        (Js+b)(Ls+R)+K^2

Ok so I have the transfer function, which is good. My problem however is that I have no idea of how to solve this equation it looks like it is third order? I might be incorrect.
Sure this could be done numerically but I would prefer an algebraic way as I need to determine the time constant!

Any help or input would be appreciated.

Edit:
wow that was stupid... just elminate (Js+b)/(Js+b) and then it can be solved...

 

[ponjavic]

Ugh, now I can't edit it obviously my edit was wrong so the question still stands. Is this a third order differential equation? And if so how can I solve it.

Not too sure about this but it looks like I should get:

I(JLs^2+bLs+JRs+bR+k^2)=V(Js+b)

which reduces to:
JLi''+(bL+JR)i'+bR+K^2-b=VJs

integrating:
JLi'+(bL+JR)i +integral((bR+K^2-b)dt)=VJ+constant

Now... what is the constant?
This is a system where the wagon is suddenly given power so at t = 0, i = 0 but what's i'(0)?