# Education Help With Signal Analysis & Control

Discussion in 'General' started by Strudul, 7 May 2015.

1. ### Strudul~

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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

2. ### UnicornUniform November India

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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?

3. ### Strudul~

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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 :/

4. ### UnicornUniform November India

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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 :/

5. ### Strudul~

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Better then than before... or during 6. ### SkiDaveMinimodder

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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

Last edited: 7 May 2015
7. ### SkiDaveMinimodder

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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

8. ### Strudul~

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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?

Last edited: 7 May 2015