Q4Control System
Question
2 marks
Q.4. Classify the control system on the basis of damping ratio.
Answer
Based on damping ratio ζ, systems are classified as undamped (ζ = 0), underdamped (0 < ζ < 1), critically damped (ζ = 1), and overdamped (ζ > 1).
- Undamped (ζ = 0): poles purely imaginary; response oscillates continuously with constant amplitude.
- Underdamped (0 < ζ < 1): complex conjugate poles with negative real part; response is decaying oscillatory (most practical systems are designed in this range, typically ζ ≈ 0.4–0.7).
- Critically damped (ζ = 1): two equal real negative poles; response reaches the final value fastest without overshoot.
- Overdamped (ζ > 1): two unequal real negative poles; response is sluggish and non-oscillatory, slower than critical damping.