Step response worksheet with answers

Free printable Step response worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 5/(0.2s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 5/(0.2s + 1)U = 10
y(∞) =
2.Easy
t (s)y(t)3t = ?95 %

A first-order system G(s) = 12/(s + 4) receives a step input of size 1 at t = 0, starting from rest. How long does the output take to reach 95 % of its final value? Find t.

G(s) = 12/(s + 4)U = 195 %
t = s
3.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 25.5/(s² + 11s + 51) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 25.5/(s² + 11s + 51)
tp = s
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 160/(s² + 7s + 80) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 160/(s² + 7s + 80)
σ =
5.Hard
t (s)y(t)15 %

A second-order system without zeros must have a step response with 5 % overshoot. Find the damping ratio ζ.

%OS = 5 %
ζ =
6.Hard
R(s)+45s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 45/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 45/(s(s + 8))
ts = s

Answer key

  1. 1. y(∞) = 50
  2. 2. t = 0.7489 s
  3. 3. tp = 0.6897 s
  4. 4. σ = −3.5
  5. 5. ζ = 0.6901
  6. 6. ts = 1 s

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