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)?

 

[oswaler]

I understand your struggle with the theory behind using current regulation on a motor-driven wagon. It seems like you have a good understanding of the transfer function and how it relates to Newton's law in this system. However, you are unsure of how to solve the resulting equation, which appears to be third order.

One approach you could take is to use Laplace transforms to simplify the equation and then solve it algebraically. This would involve transforming the equation into the s-domain and using algebraic techniques to solve for the unknowns. Alternatively, you could use numerical methods to solve the equation, as you mentioned.

Another suggestion would be to consult with a colleague or expert in the field who may have experience with similar systems. They may be able to offer insights or suggestions on how to solve the equation or provide additional resources for you to consult.

Overall, it is important to continue to explore and seek out solutions to this problem. As a scientist, it is through experimentation and problem-solving that we make progress and advance our understanding of the world around us. Good luck with your research!