When to prefer lag/lead or PID controllers

Lag/lead compensators and PID controllers both reshape the loop, but each fits a different situation.

Prefer a phase-lead compensator when

• the system is stable but has a poor transient response (low phase margin, large overshoot, slow rise);
• you need a higher bandwidth and faster response, and some extra noise sensitivity is acceptable;
• the plant has an integrator or a double integrator (e.g. satellite or position servo) that needs phase lead to stabilise it.

Prefer a phase-lag compensator when

• the transient response is already satisfactory but the steady-state error is too large (low $K_p$, $K_v$);
• low-frequency gain must be raised without changing the crossover frequency much;
• high-frequency noise must be attenuated, and a slower response is acceptable.

A lag–lead compensator is used when both the transient and the steady-state response must be improved.

Prefer a PID controller when

• the plant model is not accurately known and the controller must be tuned on site (Ziegler–Nichols rules, for example);
• zero steady-state error to a step is needed (integral action) together with damping (derivative action);
• the plant is a process plant (temperature, pressure, flow, level) with slow dynamics or dead time, where PID is the industry standard;
• the controller must be simple, with three parameters an operator can understand.