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)400.2 s?

A first-order system G(s) = 2/(0.2s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the output y(0.2) at t = 0.2 s.

G(s) = 2/(0.2s + 1)U = 20t = 0.2 s
y(0.2) =
2.Easy
t (s)y(t)20t = ?99 %

A first-order system G(s) = 4/(0.2s + 1) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 99 % of its final value? Find t.

G(s) = 4/(0.2s + 1)U = 599 %
t = s
3.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 63/(s² + 13s + 63) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 63/(s² + 13s + 63)
%OS = %
4.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 96/(s² + 6s + 96) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 96/(s² + 6s + 96)
ts = s
5.Hard
R(s)+75s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 75/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 75/(s(s + 8))
ts = s
6.Hard
R(s)+175s(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = 175/(s(s + 12)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 175/(s(s + 12))
ts = s

Answer key

  1. 1. y(0.2) = 25.28
  2. 2. t = 0.921 s
  3. 3. %OS = 1.13 %
  4. 4. ts = 1.333 s
  5. 5. ts = 1 s
  6. 6. ts = 0.6667 s

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