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)0.50.175 s?

A first-order system G(s) = 2/(s + 4) receives a step input of size 1 at t = 0, starting from rest. Find the output y(0.175) at t = 0.175 s.

G(s) = 2/(s + 4)U = 1t = 0.175 s
y(0.175) =
2.Easy
t (s)y(t)10t = ?90 %

A first-order system G(s) = 0.5/(5s + 1) receives a step input of size 20 at t = 0, starting from rest. How long does the output take to reach 90 % of its final value? Find t.

G(s) = 0.5/(5s + 1)U = 2090 %
t = s
3.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 82/(s² + 10s + 82) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 82/(s² + 10s + 82)
ts = s
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 18/(s² + s + 9) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 18/(s² + s + 9)
σ =
5.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 12))%OS = 30 %
K =
6.Hard
+−24 VR = 9 ΩL = 100 mHC = 47 µFvC​

A series RLC circuit with R = 9 Ω, L = 100 mH and C = 47 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 = 9 ΩL = 100 mHC = 47 µFV = 24 V
vC,max = V

Answer key

  1. 1. y(0.175) = 0.2517
  2. 2. t = 11.51 s
  3. 3. ts = 0.8 s
  4. 4. σ = −0.5
  5. 5. K = 281.1
  6. 6. vC,max = 41.64 V

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