The circuit diagram of an electrical network is given in figure. What type of compensator is this?

Concept:

In general, the lead and lag compensator is represented by the below transfer function

\(\frac{{{V_0}\left( s \right)}}{{{V_i}\left( s \right)}} = k\frac{{s + a}}{{s + b}}\)

If a > b then that is lag compensator because pole comes first.

If a < b then that is the lead compensator since zero comes first.

Analysis:

Lead compensator:

1) When sinusoidal input applied to this it produces sinusoidal output with the phase lead input.

2) It speeds up the Transient response and increases the margin for stability.

A circuit diagram is as shown:

Response is:

\(\frac{{{V_0}\left( s \right)}}{{{V_i}\left( s \right)}} = \frac{{{R_2}\left( {1 + s{C_1}{R_1}} \right)}}{{{R_1} + {R_2} + s{C_1}{R_1}{R_2}}}\)

\(\frac{{{V_0}\left( s \right)}}{{{V_i}\left( s \right)}} = \frac{{1 + s\tau }}{{1 + \alpha s\tau }}\)

Lead constant \(\alpha = \frac{{{R_2}}}{{{R_1} + {R_2}}}\) < 1

Important Points