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)10t = ?50 %

A first-order system G(s) = 5/(2s + 1) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 50 % of its final value? Find t.

G(s) = 5/(2s + 1)U = 250 %
t = s
2.Easy
t (s)y(t)50t = ?80 %

A first-order system G(s) = 2.5/(s + 0.5) receives a step input of size 10 at t = 0, starting from rest. How long does the output take to reach 80 % of its final value? Find t.

G(s) = 2.5/(s + 0.5)U = 1080 %
t = s
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 33/(s² + 5s + 33) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 33/(s² + 5s + 33)
tp = s
4.Medium
t (s)y(t)3

A system has the transfer function G(s) = 105/(s² + 6s + 35) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 105/(s² + 6s + 35)
ωn = rad/s
5.Hard
t (s)y(t)18 %

A second-order system without zeros must have a step response with 8 % overshoot. Find the damping ratio ζ.

%OS = 8 %
ζ =
6.Hard
R(s)+20s(s + 2)G(s)C(s)−

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

G(s) = 20/(s(s + 2))
ts = s

Answer key

  1. 1. t = 1.386 s
  2. 2. t = 3.219 s
  3. 3. tp = 0.6074 s
  4. 4. ωn = 5.916 rad/s
  5. 5. ζ = 0.6266
  6. 6. ts = 4 s

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