The primary function of the lag compensator is to increase the low frequency gain to reduce steady-state errors and decrease sensitivity to noise and parameter variations.

**To design a lag
compensator**

1.
Adjust the DC gain of the open-loop transfer function *GH*(*s*) to
satisfy low-frequency specifications. Let the adjusted gain be
*K _{c}*.

2.
Find the frequency ω_{1} for which the angle of *G*(*j*ω)
*H*(*j*ω), θ_{GH}, is equal to (-180^{o} +
θ_{M} + 5^{o}), where θ_{M} is the specified phase
margin.

The magnitude of the lag zero is
then equal to ω_{0} = 0.1 ω_{1}.

3. The ratio of the lag pole to lag zero is given by:

4.
Solve the equations in steps 3 and 4 for ω_{0} and ω_{p}.

5. The compensator transfer function is then given by:

This procedure is used to interactively design a lag compensator in the following section.