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

G(s) = 1/(2s + 1)U = 1
y(∞) =
2.Easy
t (s)y(t)252 s?

A first-order system G(s) = 5/(10s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the output y(2) at t = 2 s.

G(s) = 5/(10s + 1)U = 5t = 2 s
y(2) =
3.Medium
t (s)y(t)0.5ts​ = ?

A system has the transfer function G(s) = 7/(s² + s + 14) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 7/(s² + s + 14)
ts = s
4.Medium
t (s)y(t)3tp​ = ?

A system has the transfer function G(s) = 234/(s² + 6s + 78) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 234/(s² + 6s + 78)
tp = s
5.Hard
t (s)y(t)1tp​ = 0.8 s15 %

The step response of a second-order system without zeros shows 15 % overshoot, and the first peak occurs at t = 0.8 s. Find the natural frequency ωn.

%OS = 15 %tp = 0.8 s
ωn = rad/s
6.Hard
R(s)+230s(s + 20)G(s)C(s)−

A unity negative feedback loop has G(s) = 230/(s(s + 20)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 230/(s(s + 20))
ts = s

Answer key

  1. 1. y(∞) = 1
  2. 2. y(2) = 4.532
  3. 3. ts = 8 s
  4. 4. tp = 0.3782 s
  5. 5. ωn = 4.587 rad/s
  6. 6. ts = 0.4 s

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