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)1002 s60

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 100. At t = 2 s it reads 60. Find the time constant τ.

y(∞) = 100y(2) = 60
τ = s
2.Easy
t (s)y(t)20.4 s?

A first-order system G(s) = 5/(s + 5) receives a step input of size 2 at t = 0, starting from rest. Find the output y(0.4) at t = 0.4 s.

G(s) = 5/(s + 5)U = 2t = 0.4 s
y(0.4) =
3.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 270/(s² + 8s + 90) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 270/(s² + 8s + 90)
%OS = %
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 56/(s² + 6s + 28) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 56/(s² + 6s + 28)
%OS = %
5.Hard
+−5 VR = 175 ΩL = 100 mHC = 4.7 µFvC​

A series RLC circuit with R = 175 Ω, L = 100 mH and C = 4.7 µF is connected to a 5 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 = 175 ΩL = 100 mHC = 4.7 µFV = 5 V
tp = ms
6.Hard
R(s)+170s(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = 170/(s(s + 12)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 170/(s(s + 12))
ts = s

Answer key

  1. 1. τ = 2.183 s
  2. 2. y(0.4) = 1.729
  3. 3. %OS = 23.2 %
  4. 4. %OS = 11.51 %
  5. 5. tp = 2.692 ms
  6. 6. ts = 0.6667 s

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