Difficulty: Easy
Correct Answer: low pass filter
Explanation:
Introduction / Context:Compensators shape loop gain to meet stability and performance targets. A lag compensator is routinely used to boost low-frequency gain (improving steady-state accuracy) while minimally affecting high-frequency phase margin.
Given Data / Assumptions:
Concept / Approach:The pole is at lower frequency than the zero (|p| < |z|). Magnitude response rises at very low frequencies and then rolls off as frequency increases, which is characteristic of a low-pass filter. Phase lag is introduced mainly around the pole–zero break frequencies, hence the name “lag”.
Step-by-Step Solution:
At ω ≪ |p|: |Gc(jω)| ≈ 1; high gain at very low frequency improves steady-state accuracy.Between pole and zero: magnitude decreases; net phase lag appears.At ω ≫ |z|: |Gc(jω)| → 1/β < 1, attenuating high-frequency components like a low-pass.Verification / Alternative check:
Bode plot shows −20 dB/dec trend between pole and zero and reduced high-frequency gain, matching low-pass behavior.Why Other Options Are Wrong:
High-pass boosts high frequency—opposite to lag.Band-pass emphasizes a mid-band peak—untrue for lag.“Either (a) or (b)” contradicts distinct behavior; all-pass does not alter magnitude, only phase.Common Pitfalls:
Confusing lag with lead (lead behaves more like a high-pass around its corner frequencies).Final Answer:
low pass filter
Discussion & Comments