behaviour if roots are in poles

what will happen to a system when it's are in poles?
\ what are the parameter get affected?

electronics_kumar

Poles locations affect everything about a closed loop system including:
. Stability
. Time Response
. Frequency response
.
For a concise explanation, see the following site
~ h**p://cnx.org/content/m10112/latest/
regards,
Kral

hi.......
along with stability, pole of a closed loop system or charecteristics equation shows how much our system close to instability.............:idea:

Kral said:

electronics_kumar

Poles locations affect everything about a closed loop system including:
. Stability
. Time Response
. Frequency response
.
For a concise explanation, see the following site
~ h**p://cnx.org/content/m10112/latest/
regards,
Kral

Click to expand...

Kral go through the site mentioned by u...
but i didn't get anything about role played by locations of poles in determining time and frequency response...
//

electronics_kumar,
You are right. This site does not describe what you need. Here is a brief synopsis:
Each pole pair defines an undamped natural frequency W0. Let a, b be the real and imaginary coordinates of a pole pair. Then
W0 = sqrt(a^2 + b^2)
The "Q" of the pole pair can be expressed as
~ Q = W0/(2*alpha)
~
As Q increases, the following things happen:
~ The frequency response gets "Peakier"
~ The step response becomes more oscillatory.
~
An easier way to visualize this is; the higher the ratio of real to imaginary coordinates of a pole, the more stable (less oscillatory) the system is.
~
If the real part of the pole is positive, the system is unstable.
~
If the real coordinate of pole pair are zero (purely imaginary poles), the system oscillates.
~
Real negative poles are stable, and exhibit no overshoot.
~
This explanation is highly simplified. For more details see any book on classical control systems or analog filter design.
~
This discussion is for analog systems. The details are different for digital systems. Let me know if you need the corresponding explanation for the "z" domain.
Regards,
Kral