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)12.51 s?

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

G(s) = 2.5/(1s + 1)U = 5t = 1 s
y(1) =
2.Easy
t (s)y(t)200.375 s?

A first-order system G(s) = 4/(s + 4) receives a step input of size 20 at t = 0, starting from rest. Find the output y(0.375) at t = 0.375 s.

G(s) = 4/(s + 4)U = 20t = 0.375 s
y(0.375) =
3.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 180/(s² + 4s + 90) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 180/(s² + 4s + 90)
%OS = %
4.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 16.5/(s² + 5s + 33) and receives a unit step input. Find the damping ratio ζ.

G(s) = 16.5/(s² + 5s + 33)
ζ =
5.Hard
R(s)+275s(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 275/(s(s + 6)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 275/(s(s + 6))
ts = s
6.Hard
R(s)+290s(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 290/(s(s + 4)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 290/(s(s + 4))
ts = s

Answer key

  1. 1. y(1) = 7.902
  2. 2. y(0.375) = 15.54
  3. 3. %OS = 50.79 %
  4. 4. ζ = 0.4352
  5. 5. ts = 1.333 s
  6. 6. ts = 2 s

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