An R-C network has the transfer function \({G_C}\left( s \right) = \frac{{{s^2} + 10s + 24}}{{{s^2} + 10s + 16}}\)

The network could be used as

1. lead compensator

2. lag compensator

3. lag-lead compensator

Which of the above is/are correct?

Concept:

Pole zero plot of different compensators is given below.

Application:

\({G_C}\left( s \right) = \frac{{{s^2} + 10s + 24}}{{{s^2} + 10s + 16}}\)

\( = \frac{{\left( {s + 4} \right)\left( {s + 6} \right)}}{{\left( {s + 2} \right)\left( {s + 8} \right)}}\)

Poles: s = -2, -8

Zeros: s = -4, -6

The pole-zero plot of the above transfer function is shown below.

The above pole-zero represents that the given system is a lag-lead compensator.