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) = 2.5/(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) = 2.5/(2s + 1)U = 1
y(∞) =
2.Easy
t (s)y(t)5t = ?75 %

A first-order system G(s) = 5/(2.5s + 1) receives a step input of size 1 at t = 0, starting from rest. How long does the output take to reach 75 % of its final value? Find t.

G(s) = 5/(2.5s + 1)U = 175 %
t = s
3.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 14/(s² + 6s + 28) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 14/(s² + 6s + 28)
ωn = rad/s
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 26/(s² + 6s + 26) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 26/(s² + 6s + 26)
ωn = rad/s
5.Hard
+−10 VR = 126 ΩL = 200 mHC = 2 µFvC​

A series RLC circuit with R = 126 Ω, L = 200 mH and C = 2 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time tp of the first voltage peak, in ms.

R = 126 ΩL = 200 mHC = 2 µFV = 10 V
tp = ms
6.Hard
R(s)+120s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 120/(s(s + 2)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 120/(s(s + 2))
ts = s

Answer key

  1. 1. y(∞) = 2.5
  2. 2. t = 3.466 s
  3. 3. ωn = 5.292 rad/s
  4. 4. ωn = 5.099 rad/s
  5. 5. tp = 2.028 ms
  6. 6. ts = 4 s

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