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)0.55 s?

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

G(s) = 0.5/(5s + 1)U = 1t = 5 s
y(5) =
2.Easy
t (s)y(t)2t = ?60 %

A first-order system G(s) = 20/(s + 20) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 60 % of its final value? Find t.

G(s) = 20/(s + 20)U = 260 %
t = s
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 38/(s² + 6s + 38) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 38/(s² + 6s + 38)
tp = s
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 106/(s² + 5s + 53) and receives a unit step input. Find the damping ratio ζ.

G(s) = 106/(s² + 5s + 53)
ζ =
5.Hard
R(s)+235s(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 235/(s(s + 6)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 235/(s(s + 6))
ts = s
6.Hard
R(s)+15s(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 15/(s(s + 5)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 15/(s(s + 5))
ts = s

Answer key

  1. 1. y(5) = 0.3161
  2. 2. t = 0.04581 s
  3. 3. tp = 0.5834 s
  4. 4. ζ = 0.3434
  5. 5. ts = 1.333 s
  6. 6. ts = 1.6 s

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