The transfer function of the lead compensator is:

1
Gc(s) = \(\rm\frac{1}{\beta} \frac{s+\frac{1}{T}}{s+\frac{1}{\beta T}}\) where β < 1
2
Gc(s) = \(\rm\frac{1}{\beta} \frac{s+\frac{1}{T}}{s+\frac{1}{\beta T}}\) where β > 1
3
Gc(s) = \(\rm\frac{1}{\beta} \frac{s−\frac{1}{T}}{s−\frac{1}{\beta T}}\) where β > 1
4
Gc(s) = \(\rm\frac{1}{\beta} \frac{s−\frac{1}{T}}{s−\frac{1}{\beta T}}\) where β < 1

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