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)200.5 s?

A first-order system G(s) = 2/(s + 2) receives a step input of size 20 at t = 0, starting from rest. Find the output y(0.5) at t = 0.5 s.

G(s) = 2/(s + 2)U = 20t = 0.5 s
y(0.5) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 10/(s + 20) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 10/(s + 20)U = 10
y(∞) =
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 84/(s² + 13s + 84) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 84/(s² + 13s + 84)
σ =
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 46/(s² + 6s + 23) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 46/(s² + 6s + 23)
%OS = %
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
R(s)+120s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 120/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 120/(s(s + 8))
ts = s

Answer key

  1. 1. y(0.5) = 12.64
  2. 2. y(∞) = 5
  3. 3. σ = −6.5
  4. 4. %OS = 8.055 %
  5. 5. K = 281.1
  6. 6. ts = 1 s

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