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) = 10/(2.5s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 10/(2.5s + 1)U = 20
y(∞) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 4/(10s + 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/(10s + 1)U = 5
y(∞) =
3.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 26/(s² + 2s + 13) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 26/(s² + 2s + 13)
ts = s
4.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 96/(s² + 13s + 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 + 13s + 96)
ts = s
5.Hard
R(s)+100s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 100/(s(s + 2)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 100/(s(s + 2))
ts = s
6.Hard
R(s)+45s(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 45/(s(s + 6)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 45/(s(s + 6))
ts = s

Answer key

  1. 1. y(∞) = 200
  2. 2. y(∞) = 20
  3. 3. ts = 4 s
  4. 4. ts = 0.6154 s
  5. 5. ts = 4 s
  6. 6. ts = 1.333 s

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