PG1995
Active Member
Hi
Q1:
For a system to be stable all of its poles should lie to the left of imaginary axis of the s-plane; even if one pole lies to the right of the s-plane it would make the system unstable. If poles lie on the imaginary axis then the system is marginally stable. This is the criteria which is given in most places. But I have also been told that for a stable system the number of zeros and poles should be equal. I have found some sources which indirectly also support this. For instance, check out this source:
**broken link removed**
But the issue is that I have seen many functions which don't have equal number of zeros and poles but still are considered stable (please don't forget that I'm just a newbie to the Laplace). For example, s/(s+2)(s+3) has poles at s=-2, -3 and zero at s=0. It's considered stable in spite of the fact that number of poles doesn't equal number of zeros in this case. You can also check this source. This another source summarizes the stability this way.
The significance of zeros is explained after 10:25 in link #1 below.
Q2:
How do I interpret poles and zeros physically in context of circuits? I understand that mathematically poles are roots of denominator and zeros are roots of numerator of a transfer function, H(s) = N(s)/D(s) = Y(s)/X(s). My complete question is here.
Thanks a lot.
Regards
PG
Useful links:
1: https://www.youtube.com/watch?v=5jYr0QktWxE (very good for understanding poles and zeroes)
2: https://www.youtube.com/watch?v=ZGPtPkTft8g (laplace transform, good one)
3: https://www.youtube.com/watch?v=UFPhhS3MCiM (feedback control example, okay)
4: https://www.youtube.com/watch?v=KFbUr5Vy_cc (poles zeroes final value theorem, okay)
5: https://www.youtube.com/watch?v=CgQBfjD-4uk (stability and pole location, very good one)
6: https://www.youtube.com/watch?v=cQdIVwKqj2M (poles and zeroes, good one)
7: https://www.youtube.com/watch?v=pSN7t79RxC4 (MIT lecture, laplace transform, good one)
8: https://www.youtube.com/watch?v=2BjZOeYJeZ0 (stability, okay)
9: https://www.electro-tech-online.com/custompdfs/2013/03/PoleZero.pdf
10: https://en.wikipedia.org/wiki/Pole–zero_plot
11: https://en.wikipedia.org/wiki/Pole_(complex_analysis)
Q1:
For a system to be stable all of its poles should lie to the left of imaginary axis of the s-plane; even if one pole lies to the right of the s-plane it would make the system unstable. If poles lie on the imaginary axis then the system is marginally stable. This is the criteria which is given in most places. But I have also been told that for a stable system the number of zeros and poles should be equal. I have found some sources which indirectly also support this. For instance, check out this source:
**broken link removed**
But the issue is that I have seen many functions which don't have equal number of zeros and poles but still are considered stable (please don't forget that I'm just a newbie to the Laplace). For example, s/(s+2)(s+3) has poles at s=-2, -3 and zero at s=0. It's considered stable in spite of the fact that number of poles doesn't equal number of zeros in this case. You can also check this source. This another source summarizes the stability this way.
The significance of zeros is explained after 10:25 in link #1 below.
Q2:
How do I interpret poles and zeros physically in context of circuits? I understand that mathematically poles are roots of denominator and zeros are roots of numerator of a transfer function, H(s) = N(s)/D(s) = Y(s)/X(s). My complete question is here.
Thanks a lot.
Regards
PG
Useful links:
1: https://www.youtube.com/watch?v=5jYr0QktWxE (very good for understanding poles and zeroes)
2: https://www.youtube.com/watch?v=ZGPtPkTft8g (laplace transform, good one)
3: https://www.youtube.com/watch?v=UFPhhS3MCiM (feedback control example, okay)
4: https://www.youtube.com/watch?v=KFbUr5Vy_cc (poles zeroes final value theorem, okay)
5: https://www.youtube.com/watch?v=CgQBfjD-4uk (stability and pole location, very good one)
6: https://www.youtube.com/watch?v=cQdIVwKqj2M (poles and zeroes, good one)
7: https://www.youtube.com/watch?v=pSN7t79RxC4 (MIT lecture, laplace transform, good one)
8: https://www.youtube.com/watch?v=2BjZOeYJeZ0 (stability, okay)
9: https://www.electro-tech-online.com/custompdfs/2013/03/PoleZero.pdf
10: https://en.wikipedia.org/wiki/Pole–zero_plot
11: https://en.wikipedia.org/wiki/Pole_(complex_analysis)
Attachments
Last edited: