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)501 s?

A first-order system G(s) = 2.5/(s + 0.5) receives a step input of size 10 at t = 0, starting from rest. Find the output y(1) at t = 1 s.

G(s) = 2.5/(s + 0.5)U = 10t = 1 s
y(1) =
2.Easy
t (s)y(t)10t = ?50 %

A first-order system G(s) = 2.5/(s + 0.5) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 50 % of its final value? Find t.

G(s) = 2.5/(s + 0.5)U = 250 %
t = s
3.Medium
t (s)y(t)3

A system has the transfer function G(s) = 57/(s² + 7s + 19) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 57/(s² + 7s + 19)
σ =
4.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 80/(s² + 10s + 40) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 80/(s² + 10s + 40)
ts = s
5.Hard
R(s)+Ks(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 16)). Find the gain K that gives a step response with 10 % overshoot.

G(s) = K/(s(s + 16))%OS = 10 %
K =
6.Hard
R(s)+300s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 300/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 300/(s(s + 8))
ts = s

Answer key

  1. 1. y(1) = 19.67
  2. 2. t = 1.386 s
  3. 3. σ = −3.5
  4. 4. ts = 0.8 s
  5. 5. K = 183.1
  6. 6. ts = 1 s

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