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) = 0.5/(0.8s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 0.5/(0.8s + 1)U = 10
y(∞) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 2.5/(4s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(4s + 1)U = 5
y(∞) =
3.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 62/(s² + 10s + 62) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 62/(s² + 10s + 62)
%OS = %
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 96/(s² + 5s + 48) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 96/(s² + 5s + 48)
σ =
5.Hard
t (s)y(t)120 %

A second-order system without zeros must have a step response with 20 % overshoot. Find the damping ratio ζ.

%OS = 20 %
ζ =
6.Hard
R(s)+Ks(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 16)). Find the gain K that gives a step response with 2 % overshoot.

G(s) = K/(s(s + 16))%OS = 2 %
K =

Answer key

  1. 1. y(∞) = 5
  2. 2. y(∞) = 12.5
  3. 3. %OS = 7.559 %
  4. 4. σ = −2.5
  5. 5. ζ = 0.4559
  6. 6. K = 105.3

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