How to design lead lag compensator?
This type of compensator is designed by determining a from the amount of phase needed to satisfy the phase margin requirements, and determing T to place the added phase at the new gain-crossover frequency. Another effect of the lead compensator can be seen in the magnitude plot.
How does a lead lag compensator work?
The lead compensator provides phase lead at high frequencies. This shifts the root locus to the left, which enhances the responsiveness and stability of the system. The lag compensator provides phase lag at low frequencies which reduces the steady state error.