Question

A unity feedback control system has \(G(s) = \frac{K}{{{s^2}\left( {sT + 1} \right)}}\)

The order and type of the closed-loop system will be:

1. 3 and 3
2. 2 and 3
3. 1 and 3
4. 3 and 2

Answer 1

Correct Answer - Option 4 : 3 and 2

Concept:

Poles of closed-loop system = zeroes of the characteristic equation.

Characteristic equation is given by:

1 + G(s) H(s) = 0

Order: Highest power of characteristic equation.

Type: It is obtained by observing the number of open loop poles occuring at origin.

Analysis:

\(G(s) = \frac{K}{{{s^2}\left( {sT + 1} \right)}}\)

H(s) = 1

The characteristic equation will be:

\(1 + \frac{k}{{{s^2}\left( {sT + 1} \right)}} = 0\)

s² (sT + 1) + k = 0

s³ T + s² + k = 0

The highest power of the above characteristic equation is 3

So, order = 3

Type = 2