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

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

A first-order system G(s) = 0.5/(s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 0.5/(s + 1)U = 5
y(∞) =
3.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 2.5/(s² + 2s + 5) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 2.5/(s² + 2s + 5)
%OS = %
4.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 36/(s² + 8s + 72) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 36/(s² + 8s + 72)
tp = s
5.Hard
t (s)y(t)150 %

A second-order system without zeros must have a step response with 50 % overshoot. Find the damping ratio ζ.

%OS = 50 %
ζ =
6.Hard
R(s)+155s(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 155/(s(s + 4)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 155/(s(s + 4))
ts = s

Answer key

  1. 1. y(∞) = 1
  2. 2. y(∞) = 2.5
  3. 3. %OS = 20.79 %
  4. 4. tp = 0.4198 s
  5. 5. ζ = 0.2155
  6. 6. ts = 2 s

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