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How can we know if the system is oscillating and if it is decaying with only a quadratic equation?
PS:
<1> Do not involve any calculus
<2> Haven't learnt damping.
 one year ago
 one year ago
How can we know if the system is oscillating and if it is decaying with only a quadratic equation? PS: <1> Do not involve any calculus <2> Haven't learnt damping.
 one year ago
 one year ago

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ash2326Best ResponseYou've already chosen the best response.1
First of all find the closed loop transfer function of the system
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Suppose it is \[Y= \frac{1}{1kz^{1} + bz^{2}}\]where k is an unknown constant and b is a known constant.
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
I meant \[\frac{Y}{X}=...\]
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Solving the denominator =0, \[1kz^{1}+bz^{2}=0\]\[z^2  kz + b =0\]\[z = \frac{k \pm \sqrt{k^2  4b}}{2}\]
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
You'd need to find the poles of the system, sorry I was dealing in the s domain
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Poles are at \[\frac{k\pm\sqrt{k^24b}}{2}\]
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
There will be many cases, \[ K=2\sqrt b, K>2\sqrt b\ and\ K<2\sqrt b\] for first case, \[z= \sqrt b\] if b<1 then system will decay if b=1 system will be constant if b>1 then system will be unbounded.
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
@Callisto I found a good document on this, please see it. You'll understand better http://www.eng.ox.ac.uk/~conmrc/dcs/dcslec4.pdf
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
Let me know if you have doubt anywhere
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Now, I see why I can never get the answer. The reason why I have been stressing that no calculus is involved is because when we learnt this topic, our lecturer didn't not teach us using calculus, i.e. solving D.E., using expressions in exponential forms, nor mentioning those fancy terms like damping. Anyway, thanks for trying to help!
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
so you undestood now ?
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
oops, did you ask this doubt to your teacher?
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Ha! I don't even have to ask as in the lecture, he has written "you will find out the reason if you take EEE"
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
*in the lecture notes
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
umm, where did calculus was used?
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
He has NEVER used calculus in this course.
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
But the solution requires just solving the quadratics. then depending on the poles, we classify the system
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
p = pole p = 1 => remains (unchanged) p >1 => diverge p < 1 => converge
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
now you need to check which one lies in, out or on the unit circle. then you can classify the system
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
@Callisto are you here?
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
checking the magnitude? I did it. But the problem is how I can identify if the system oscillates. Sorry, I was on other page.
 one year ago

ash2326Best ResponseYou've already chosen the best response.1
if the poles are on the unit circle, system will oscillate if they are inside, it'll decay if they are outside, oscillations will grow unboundedly
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
Hmm... I think the magnitude of the pole only tell us if the system is converging/diverging/remaining unchanged?!
 one year ago

CallistoBest ResponseYou've already chosen the best response.0
I think I understand how to analyze the system now, thanks :)
 one year ago
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