How do lead and lag differ in pole-zero position?

Lead: zero nearer the origin; lag: pole nearer the origin

Lead: pole nearer the origin; lag: zero nearer the origin

Both have zero nearer the origin

Both have pole nearer the origin

What do lead and lag do to bandwidth and gain crossover frequency?

Lead increases both; lag decreases both

Lead decreases both; lag increases both

When is a lag compensator the right choice?

Transient is acceptable but steady-state error is too large

The system is too slow or oscillatory

Noise sensitivity must be increased

2072 Chaitra · 4 marks

Compare lag and lead compensator applications

Short answer

Lead compensator (zero nearer origin): phase lead, increased bandwidth, faster response, improved transient and stability, passes high-frequency noise. Lag compensator (pole nearer origin): low-frequency gain boost, improved steady-state accuracy, reduced bandwidth, slower response, attenuates high-frequency noise.

Compare the Lag and Lead compensator applications in control system.

A lead compensator $G_c(s) = \dfrac{s+z}{s+p}$ with $p > z$ adds positive phase near the gain crossover and mainly improves the transient response. A lag compensator with $p < z$ , both close to the origin, adds low-frequency gain and mainly improves steady-state accuracy.

Point	Lead compensator	Lag compensator
Pole–zero position	Zero nearer the origin than the pole	Pole nearer the origin than the zero
Phase added	Positive (phase lead)	Negative (phase lag), kept small
Main purpose	Better transient response and stability	Better steady-state error ( $K_p$ , $K_v$ , $K_a$ )
Effect on bandwidth	Increases bandwidth, faster response	Reduces bandwidth, slower response
Gain crossover frequency	Moves to a higher value	Moves to a lower value
Phase margin	Raised directly by the phase lead	Raised by lowering the crossover frequency
Effect on noise	Passes more high-frequency noise	Filters (attenuates) high-frequency noise
Root locus	Pulls the locus to the left (more stable)	Locus nearly unchanged near dominant poles
Network type	Acts like a high-pass filter (like PD)	Acts like a low-pass filter (like PI)

Where each is used:

Lead: when the system is too slow or too oscillatory, e.g. reducing overshoot and settling time of a position servo, or adding phase margin to a type-1 or type-2 plant.
Lag: when the transient response is already acceptable but the steady-state error is too large, e.g. raising $K_v$ of a tracking antenna or a temperature controller by about 10 times without changing the overshoot.
When both transient and steady-state performance must improve, a lag–lead compensator is used.

✓ Answer checked by Claude Opus 5.5 (high effort)

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