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

The network could be used as

1. lead compensator

2. lag compensator

3. lag-lead compensator
Which of the above is/are correct?

Question

Question

This question was previously asked in

ESE Electrical 2016 Paper 1: Official Paper

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Answer 1

Concept:

Pole zero plot of different compensators is given below.

Compensator	Pole zero plot	Important
Lag		Pole is near to the origin. Pole is dominant.
Lead		Zero is near to the origin. Zero is dominant.
Lag-lead		Lag system is dominant. Lag system is near to the origin.

Application:

$G_{C} (s) = \frac{s^{2} + 10 s + 24}{s^{2} + 10 s + 16}$

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

Poles: s = -2, -8

Zeros: s = -4, -6

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

F1 U.B Madhu 27.06.20 D12

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