For a stable system, poles of the transfer function
A. should lie entirely in the right half of the s-plane
B. should lie on the Y-axis
C. should lie entirely in the left half of the s-plane
D. should lie at the origin
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Explanation:
The poles location and system response along with the stability is given below:
|
Pole location |
Transfer function |
System response (approx.) |
Stability |
|
Left of s-plane
|
\(\frac{k}{{\left( {S + a} \right)\left( {S + b} \right)}}\) |
|
Stable always |
|
On the jw axis
|
\(\frac{k}{{{S^2} + {a^2}}}\) |
|
Marginal stable |
|
Right of s-plane
|
\(\frac{k}{{\left( {S - a} \right)\left( {S - b} \right)}}\) |
|
Unstable always |
Conclusion:
1) System stability is always decided by the location of poles irrespective of zeroes location.
2) For a stable system, poles of the transfer function should be in the left of the s-plane.
