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)202 s12

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 2 s it reads 12. Find the time constant τ.

y(∞) = 20y(2) = 12
τ = s
2.Easy
t (s)y(t)101 s?

A first-order system G(s) = 0.5/(2s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the output y(1) at t = 1 s.

G(s) = 0.5/(2s + 1)U = 20t = 1 s
y(1) =
3.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 34/(s² + 5s + 34) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 34/(s² + 5s + 34)
%OS = %
4.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 44.5/(s² + 9s + 89) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 44.5/(s² + 9s + 89)
%OS = %
5.Hard
R(s)+125s(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 125/(s(s + 6)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 125/(s(s + 6))
ts = s
6.Hard
t (s)y(t)18 %

A second-order system without zeros must have a step response with 8 % overshoot. Find the damping ratio ζ.

%OS = 8 %
ζ =

Answer key

  1. 1. τ = 2.183 s
  2. 2. y(1) = 3.935
  3. 3. %OS = 22.52 %
  4. 4. %OS = 18.18 %
  5. 5. ts = 1.333 s
  6. 6. ζ = 0.6266

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