Question

Please help me with part (b.) of problem #2 of the attached file.

Answer 1

I developed this in part (a.) of problem #2...

\[\tau _{m}(s)=\frac{ K _{m}^{2} s }{ R+Ls }\Omega _{m}(s)-\frac{ K _{m} }{ R+Ls }V _{s}(s)\]

Answer 2

What is meant by "assume a current source is driving the motor"?

How do I get V(s) in terms of I(s)?

Answer 3

Hi.
I see that you're working through sheets on control engineering at Illinois. Interesting stuff, and I think it's rooted in Laplace transforms. So, if you work out the transfer functions of each component you can multiply them together to work out the overall TF of the system. They're sort of "packaged up" differential equations using e (expo) and complex numbers to confuse, irritate and bamboozle. Finally, though, once you've worked out the TF for a component - for an inductor TF(L )= j omega TF (L) = sL, for a capacitor TF(C)=1/j omega C = 1/sC then it should be an algebraic multiplying job. I think that's the idea behind these shenanigans.
Bon chance et bon voyage.

Answer 4

ps the I "asked jeeves" and the engine came up with these links which may help

https://en.wikipedia.org/wiki/Control_engineering

http://www.freestudy.co.uk/control/t1.pdf

http://controlmanuals.com/files/Automation/Control-Engineering/INSTRUMENTATION-AND-CONTROL----TUTORIAL--CONTROL-
ACTION-~pdf1062.html

http://www.freestudy.co.uk/control/t11.pdf