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)203 s8

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 3 s it reads 8. Find the time constant τ.

y(∞) = 20y(3) = 8
τ = s
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 20/(s + 20) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 20/(s + 20)U = 5
y(∞) =
3.Medium
t (s)y(t)2

A system has the transfer function G(s) = 152/(s² + 12s + 76) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 152/(s² + 12s + 76)
σ =
4.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 70/(s² + 7s + 70) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 70/(s² + 7s + 70)
%OS = %
5.Hard
R(s)+Ks(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 4)). Find the gain K that gives a step response with 15 % overshoot.

G(s) = K/(s(s + 4))%OS = 15 %
K =
6.Hard
+−24 VR = 63 ΩL = 200 mHC = 2 µFvC​

A series RLC circuit with R = 63 Ω, L = 200 mH and C = 2 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage vC,max.

R = 63 ΩL = 200 mHC = 2 µFV = 24 V
vC,max = V

Answer key

  1. 1. τ = 5.873 s
  2. 2. y(∞) = 5
  3. 3. σ = −6
  4. 4. %OS = 23.53 %
  5. 5. K = 14.97
  6. 6. vC,max = 41.52 V

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