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)105 s?

A first-order system G(s) = 0.5/(2.5s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the output y(5) at t = 5 s.

G(s) = 0.5/(2.5s + 1)U = 20t = 5 s
y(5) =
2.Easy
t (s)y(t)201.25 s?

A first-order system G(s) = 10/(2.5s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the output y(1.25) at t = 1.25 s.

G(s) = 10/(2.5s + 1)U = 2t = 1.25 s
y(1.25) =
3.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 18/(s² + 5s + 18) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 18/(s² + 5s + 18)
%OS = %
4.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 60/(s² + 4s + 60) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 60/(s² + 4s + 60)
%OS = %
5.Hard
R(s)+105s(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = 105/(s(s + 16)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 105/(s(s + 16))
ts = s
6.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 =

Answer key

  1. 1. y(5) = 8.647
  2. 2. y(1.25) = 7.869
  3. 3. %OS = 10.11 %
  4. 4. %OS = 43.19 %
  5. 5. ts = 0.5 s
  6. 6. ζ = 0.2155

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