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) = 4/(5s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 4/(5s + 1)U = 2
y(∞) =
2.Easy
t (s)y(t)25t = ?60 %

A first-order system G(s) = 5/(0.8s + 1) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 60 % of its final value? Find t.

G(s) = 5/(0.8s + 1)U = 560 %
t = s
3.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 15.5/(s² + 6s + 31) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 15.5/(s² + 6s + 31)
tp = s
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 14/(s² + s + 14) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 14/(s² + s + 14)
ωn = rad/s
5.Hard
R(s)+200s(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = 200/(s(s + 16)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 200/(s(s + 16))
ts = s
6.Hard
R(s)+295s(s + 20)G(s)C(s)−

A unity negative feedback loop has G(s) = 295/(s(s + 20)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 295/(s(s + 20))
ts = s

Answer key

  1. 1. y(∞) = 8
  2. 2. t = 0.733 s
  3. 3. tp = 0.6698 s
  4. 4. ωn = 3.742 rad/s
  5. 5. ts = 0.5 s
  6. 6. ts = 0.4 s

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