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) = 5/(s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 5/(s + 1)U = 10
y(∞) =
2.Easy
t (s)y(t)y(∞) = ?

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

G(s) = 2/(s + 2)U = 1
y(∞) =
3.Medium
t (s)y(t)2

A system has the transfer function G(s) = 92/(s² + 9s + 46) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 92/(s² + 9s + 46)
σ =
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 62/(s² + 11s + 62) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 62/(s² + 11s + 62)
ωn = rad/s
5.Hard
+−12 VR = 196 ΩL = 500 mHC = 4.7 µFvC​

A series RLC circuit with R = 196 Ω, L = 500 mH and C = 4.7 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage vC,max.

R = 196 ΩL = 500 mHC = 4.7 µFV = 12 V
vC,max = V
6.Hard
R(s)+75s(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 75/(s(s + 6)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 75/(s(s + 6))
ts = s

Answer key

  1. 1. y(∞) = 50
  2. 2. y(∞) = 1
  3. 3. σ = −4.5
  4. 4. ωn = 7.874 rad/s
  5. 5. vC,max = 16.46 V
  6. 6. ts = 1.333 s

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