Design lead compensator

1. How is lead compensator calculated?
2. Why do we need to design a compensator?

How is lead compensator calculated?

A lead compensator in frequency response form is given by the following. with p =1 / T, z = 1 / aT, and Kc = a. In frequency response design, the phase-lead compensator adds positive phase to the system over the frequency range 1 / aT to 1 / T.

Why do we need to design a compensator?

Lag compensators are intended for improving steady state response - in other words, we are focused on tuning the DC gain in the magnitude plot. Conversely, lead compensators are trying to meet transient performance specifications, which means that they need to change the phase diagram to add phase margin.