Hey I'm trying to revise for my signal analysis and control exam, but I'm having trouble with a few of the questions. No matter how much I read through my notes and search on the internet, I can't work them out. If anyone could explain them to me or at least point me in the right direction it would be greatly appreciated. 1a) I think I'm right in saying that Ta(s) / Vf(s) = K/ (1+Ts) But then I have no idea how to calculate K. For T, can I just say T = L/R (because it's an inductor)? 1b) Honestly not a clue where to start here... 2a) From what I can work out, the OLTF = G(s)H(s) and CLTF = [G(s)H(s)] / [1+ G(s)H(s)] So, CLTF would be: ? Then I would need to rearrange it and sub the values of a,b and c in? But then why am I told what the gain is? Or am I completely off track and should be doing Laplace or something? 2b) Absolutely no idea and I'm assuming I need to know the answer to part a) to do it. 3a) 3b) Really don't know. Cheers xTatic
I'll have a look through my notes when I get a few minutes, I studied a module similar to that in Mechatronics. What year are you in?
2nd Year In 1st year we were given past questions and solutions that I could work through, but this year they are refusing to provide them for some reason and it's making it so much harder :/
Yeah I think I took that in 2nd year as well. I'll try to help but it's been a while! I tend to forget a lot of theory the week after the exam :/
I can't remember how to do q1. q2 a: CLTF = [G_c(s)G_c(s)H(s)] / [1+ G_c(s)G_c(s)H(s)] = [k_p / (s+a)(s+b)(s+c)] / [1+ k_p / (s+a)(s+b)(s+c)] q2b: You need to get the Closed Loop Characteristic Equation (CLCE). As the question hasn't said otherwise you can assume unity H(s). ie H(s)=1 CLCE: 1+ G_c(S)G_p(s) = 1+ k_p / (s+a)(s+b)(s+c) sub in the values and rearrange into a cubic. They gave you one of the roots so that you only have to find the roots of a quadratic. I can't remember how to prove stability. I'll have another look at my notes and get back to you EDIT: To show stability all the roots of the CLCE have to have negative real parts
For q3a: The steady state error is given by: e = r / [1 + G(0)] In this case r=1 as it is a unit step. so e = 1 / [1 + k.G(0)] q3b: you have to show the e = 0 when e = 1 / [1 + (k + ki/s).G(s)] when s=0
Thanks Dave. Really helped. 2a) That seems like a very easy 7 marks. 2b) Rearranging and subbing the values, I got: s^3 + 8s^2 + 6s + 260 = 0 (s+10)(s^2 -2s + 26) = 0 (s^2 -2s +26) only has imaginary roots, therefore the system is unstable. 3a) Subbing s = 0 into the OLTF gave G(0) = A. Which fit nicely to give the correct error. 3b) I'm still kinda stuck on how to prove this one. Am I okay to use my result from part a) and sub G(s) = A? Giving 1/ [1 + (K+ Ki/s)A] But then I have something divided by s, which would be divided by 0, which I can't do.... I tried rearranging, multiplying and factoring things, but I couldn't seem to be able to get it to a point where i can sub s=0 in. What am I missing here?
