The transfer function of the lead compensator is:
1
\({G_c}\left( s \right) = \frac{1}{\beta }\frac{{s + \frac{1}{T}}}{{s + \frac{1}{{\beta T}}}}\) Where β < 1
2
\({G_c}\left( s \right) = \frac{1}{\beta }\frac{{s - \frac{1}{T}}}{{s - \frac{1}{{\beta T}}}}\) Where β > 1
3
\({G_c}\left( s \right) = \frac{1}{\beta }\frac{{s + \frac{1}{T}}}{{s + \frac{1}{{\beta T}}}}\) Where β > 1
4
\({G_c}\left( s \right) = \frac{1}{\beta }\frac{{s - \frac{1}{T}}}{{s - \frac{1}{{\beta T}}}}\) Where β < 1