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) = 4/(5s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 4/(5s + 1)U = 5
y(∞) =
2.Easy
t (s)y(t)50.1 s?

A first-order system G(s) = 0.5/(0.2s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the output y(0.1) at t = 0.1 s.

G(s) = 0.5/(0.2s + 1)U = 10t = 0.1 s
y(0.1) =
3.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 56/(s² + 3s + 56) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 56/(s² + 3s + 56)
%OS = %
4.Medium
t (s)y(t)0.5ts​ = ?

A system has the transfer function G(s) = 28/(s² + 4s + 56) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 28/(s² + 4s + 56)
ts = s
5.Hard
R(s)+190s(s + 20)G(s)C(s)−

A unity negative feedback loop has G(s) = 190/(s(s + 20)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 190/(s(s + 20))
ts = s
6.Hard
R(s)+20s(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 20/(s(s + 4)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 20/(s(s + 4))
ts = s

Answer key

  1. 1. y(∞) = 20
  2. 2. y(0.1) = 1.967
  3. 3. %OS = 52.58 %
  4. 4. ts = 2 s
  5. 5. ts = 0.4 s
  6. 6. ts = 2 s

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