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> Control Systems, Cascaded Systems
anshumangaur
Posted: October 25, 2013 08:07 am
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Hi,
I am an ECE engineer studying Control systems.
I need assistance with a problem mentioned below:

Prob - Two identical first order systems have been cascaded non-interactively. The unit response of the system will be:

[a] overdamped [b] underdamped [c] undamped [d] critically damped.

Respose with good explanation on the subject matter will be highly appreciated.

Thanks.
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Geek
Posted: October 25, 2013 10:02 am
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Sounds like homework rolleyes.gif


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anshumangaur
Posted: October 25, 2013 10:44 am
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No its not actually. I am preparing for a competitive examination, and was going through a set of practice tests.
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kellys_eye
Posted: October 25, 2013 01:44 pm
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.... in which case please provide us with YOUR interpretation of the answers and we'll happily critique them.


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anshumangaur
Posted: October 25, 2013 02:29 pm
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Well that's the thing.. the answer given is 'critically damped'. But I have no idea how. I have not been able to comprehend this question properly and need assistance with the same.
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Geek
Posted: October 25, 2013 09:21 pm
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I know what that means when it comes to amplifiers and speakers, but not in your context unsure.gif


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kellys_eye
Posted: October 25, 2013 10:27 pm
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Have a read of the following: if you are still confused, get back to us...

http://www.digilentinc.com/Classroom/RealA...apter_2p4p1.pdf


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draget
Posted: October 26, 2013 03:47 am
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You know the definition of the damping factor right? Get the transfer functions for two identical first order systems, convolve/multiply them together and see what comes out smile.gif
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Sch3mat1c
Posted: October 26, 2013 03:58 am
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First order systems are single pole.

Identical first order systems are the same pole.

Cascaded (not interacting) first order systems are the product, i.e., a two equal poles.

Review definition.


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anshumangaur
Posted: October 26, 2013 08:12 am
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I think I got it.
Consider a first order system - 1/(s+a); a>0.
Cascaded system - 1/(s+a)^2.
This has an equal double pole - which is nothing but critically damped.
Correct me if I am wrong and thanks to everyone for assisting.

PS - the 'unit response' has nothing to do with the response in terms of damping, right? Its just the pole positioning in the characteristic equation.

This post has been edited by anshumangaur on October 26, 2013 08:14 am
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Sch3mat1c
Posted: October 26, 2013 04:17 pm
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Guessing "unit response" is either unit pole (a = 1) or unity gain (H = a / (s + a). Doesn't matter in any case.

Tim


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anshumangaur
Posted: October 27, 2013 06:46 pm
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I have another question.

Consider the forward path gain = K/s(s+2)(s+8) has a unity feedback.
By a suitable choice of scalar parameter K, the system can be made to oscillate at a frequency of?

My interpretation:

Considering the closed loop transfer function CE = s^3+10s^2+16s+K=0.
How should I approach to finding the frequency at which this oscillates?
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Sch3mat1c
Posted: October 28, 2013 01:54 am
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Again, look up definitions. We aren't doing homework wink.gif


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