Automatic Control Systems
A system is highly oscillatory if

Gain margin is close to 1 or phase margin is zero
Gain margin is high
Gain margin is close to 1
Gain margin is high and phase margin is 180°

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Automatic Control Systems
A lag compensator

Speeds up the transient response of the system
Improves steady state behavior of the system
Improves steady state behavior and speeds up the transient response of the system
Improves steady state behavior and preserves the transient response of the system

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