Question

The step response of a circuit is seen to have an oscillatory behaviour at the output with oscillations dying down after some time. The correct inference(s) regarding the transfer function from input to output is/are
1. that it is of at least second order.
2. that it has at least one pole-pair that is underdamped.
3. that it does not have a real pole.
4. that it is a first order system.

Answer 1

Correct Answer - Option :

Transfer function:

A transfer function (also known as system function or network function) of an electronic or control system component is a mathematical function that theoretically models the device's output for each possible input.

Second-order Transfer function:

The power of ‘s’ is two in the denominator term. This transfer function is of the second-order and the system is said to be the second-order system.

\(\frac{{C\left( s \right)\;}}{{R\left( {s\;} \right)}} = \frac{{\omega _n^2}}{{{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\)

• Pole pairs lying on the left of jw axis will be sable while on the right side system will be unstable.
• Conjugate pole Pairs on the left of jw axis are absolutely stable.
   

At least one pole-pair that is underdamped means at least one pole pair must lie on the left of jw axis.