The poles of an oscillator:
A. lie on the imaginary axis.
B. lie on unit circle centered at origin in s-plane
C. lie on the left half of s-plane
D. lie on the right half of s-plane
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
- If the poles are real and left side of s-plane, the step response approaches a steady-state value without any oscillations.
- If the poles are the complex and left side of the s-plane, the step response approaches a steady-state value with the damped oscillations.
- If poles are non-repeated on the jω axis, the step response will have fixed amplitude oscillations.
- If the poles are the real and right side of the s-plane, the step response reaches infinity without any oscillations.
- If the poles are the real and right side of the s-plane, the step response reaches infinity without any oscillations.
The plot when the poles lie on the jω axis is explained with the help of the following diagram:
The stability of the system for different pole positions is as shown:
|
Pole location |
T.F |
System stability |
|
|
\(\frac{1}{{s + a}}\) |
Stable |
|
|
\(\frac{1}{s}\) |
Marginally stable |
|
|
\(\frac{1}{{s - a}}\) |
Unstable |
|
|
\(\frac{1}{{{{\left( {s + a} \right)}^2}}}\) |
stable |
|
|
\(\frac{1}{{{s^2}}}\) |
unstable |
|
|
\(\frac{1}{{{{\left( {s - a} \right)}^2}}}\) |
unstable |
|
|
\(\frac{1}{{{{\left( {s + a} \right)}^2} + {b^2}}}\) |
stable |
|
|
\(\frac{1}{{{s^2} + {b^2}}}\) |
Marginally stable |
|
|
\(\frac{1}{{{{\left( {s - a} \right)}^2} + {b^2}}}\)
|
Unstable |
|
|
\(\frac{1}{{{{\left( {{s^2} + {b^2}} \right)}^2}}}\) |
Unstable |
