Homework Help: Matlab step response. Just need a quick check

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1. Jan 27, 2016

AnkleBreaker

1. The problem statement, all variables and given/known data
Could someone just quickly check my Step Reponse diagram which I made using Matlab. It does not look like the usual shape for a step response system which is making me a bit worried. I'm a fairly new to Matlab and Control Engineering

2. Relevant equations
G(s) = 3 / ((s^2) +3)

3. The attempt at a solution
This was the code which I entered in Matlab to obtain the above step response:
num = [3]
den = [1 0 3]
G=tf(num,den)
step(G)

2. Jan 27, 2016

Staff: Mentor

3. Jan 27, 2016

AnkleBreaker

Yes that's my image.. Very sorry.. I tried re uploading it and I thought it was working..

4. Jan 27, 2016

Staff: Mentor

I added more to my previous post after you replied...

5. Jan 27, 2016

AnkleBreaker

This is the new step response graph I am getting after I did like you asked

6. Jan 27, 2016

Staff: Mentor

Correction:
Code (Matlab M):
G=tf(3, [1, 0, 3])
This is probably the same as what you initially tried.

I don't know much about Control Engineering, but I do know something about Laplace transforms and such. The inverse Laplace transform of your G(s) function, $\mathcal{L}^{-1}[G(s)]$, is $\sqrt{3}\sin(\sqrt{3}t)$. That would explain the oscillation of the graph you show, but it doesn't explain either the period of this graph or the range (low to high values). The time-domain function I show has a period of $\frac{2\pi}{\sqrt{3}}$ and an amplitude of $\sqrt{3}$, meaning the values should range between $-\sqrt{3}$ and $\sqrt{3}$. For your original graph, the values range between 0 and 2, and the period seems to be right around $2\pi$. There also seems to be an upward shift by 1 unit.

7. Jan 27, 2016

AnkleBreaker

Thank you very much for your help. I'll try to ask Sir tomorrow what went wrong with my graph. One last question, on the time axis I have only put values up to 50. Is that enough or should I put more/less than 50, in your opinion

8. Jan 27, 2016

Staff: Mentor

50 should be enough, I think.

You didn't show the rest of your m-file, so perhaps there's something wrong in it. Here's a link to the documentation for step() - http://www.mathworks.com/help/control/ref/step.html

9. Jan 27, 2016

Staff: Mentor

That is a second order system with zero damping, so once it is given a jolt it will oscillate sinusoidally forever, as your graph demonstrates.

To see what to expect in terms of damping and natural frequency, compare your system's denominator s2 + 3
with the denominator for a general second-order system, viz.,
s2 + 2ζωns + ωn2

10. Jan 28, 2016

AnkleBreaker

Ohh there was no damping ratio. I get it now. That explains a lot. Thank you very much

11. Jan 28, 2016

AnkleBreaker

Thank you for all your help. User NascentOxygen's answer states that the graph oscillates infinitely due to there being an absence of a damper, which makes a lot of sense and explains a whole lot.

12. Jan 28, 2016

Staff: Mentor

So possibly there is a mistake in your denominator? Perhaps you meant the denominator to be (s + 3)^2

How was the denominator determined?

13. Jan 28, 2016

AnkleBreaker

This was part of a question. In the question they say:
Arm dynamics are represented by:
G(s) = 3 / ((s^2) +3)

So G(s) = 3 / ((s^2) +3) is part of the question and I did not derive it

And they want us to find a phase lead controller/compensator to fit required poles, which I did. I was just confused on why the step response of the original system didn't behave normally