What are lead and lag compensators and when are they used?

Lead compensator (zero before pole) adds positive phase, increasing phase margin and stability, speeding up response. Used when more phase margin is needed. Transfer function: Gc = (s+z)/(s+p), where z < p. Lag compensator (pole before zero) increases low-frequency gain without affecting high-frequency behavior, reducing steady-state error. Transfer function: Gc = (s+z)/(s+p), where z > p. Lead-lag combines both effects. These compensators are simpler alternatives to PID when full three-mode control is not needed.