What is lead compensator design?
The lead compensator increases the gain of the system at high frequencies (the amount of this gain is equal to a). This can increase the crossover frequency, which will help to decrease the rise time and settling time of the system (but may amplify high frequency noise).
How does a lead 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.