I have been dealing with the problem below for the last few days an have come up with some solutions to the questions. How ever I have come up a bit short with the 4th question. (Think i might be way off)

I have the T(S) function, and used the numbers given in Q3 but i am really unsure if I am even on track.
Any thoughts will be very grateful.
I had a quick look through the multiple threads on Laplace before posting this.


Q1) Find the differential equation for the input ea(t) and output theta l (t)


Q2) Find the system transfer function ( G(s))


Q3) If Ja=5 Jl=700 Da=2 Dl=800 N1=100 N2=1000 Ka=5 Kb=2 Ra=1. Find the time response for a unit impulse input
Used the above system transfer sunction, with Ea(S)=1

I get,

Q4) Given the plant below, with K=40, obtain the unit step response for the feedback control system,


Using given numbers from Q3 I get,

 

Hi,

That looks right, for the calculation of the complete response, although i did not check your numerical result just the math leading up to that last step.

However, the question seems to want the time response, so i guess you would have to transform that last expression into the time domain using the Inverse Laplace Transform because they say they want the time response.

Also, we usually use the lower case 's' for the Laplace variable, and when using the variable "L" for anything it usually works better to use the upper case "L" because the lower case L looks like the number 1 with a modern font.

 

MrAI

Thanks for your input. I ended up, taking the inverse Laplace transform of the of the last expression, thus getting a value for the time response.
Ill take note of using "s" and "L".