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) = 2.5/(1s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(1s + 1)U = 2
y(∞) =
2.Easy
t (s)y(t)12.55 s?

A first-order system G(s) = 2.5/(2.5s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the output y(5) at t = 5 s.

G(s) = 2.5/(2.5s + 1)U = 5t = 5 s
y(5) =
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 15/(s² + 6s + 15) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 15/(s² + 6s + 15)
σ =
4.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 55/(s² + 12s + 55) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 55/(s² + 12s + 55)
ts = s
5.Hard
R(s)+250s(s + 20)G(s)C(s)−

A unity negative feedback loop has G(s) = 250/(s(s + 20)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 250/(s(s + 20))
ts = s
6.Hard
R(s)+120s(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 120/(s(s + 5)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 120/(s(s + 5))
ts = s

Answer key

  1. 1. y(∞) = 5
  2. 2. y(5) = 10.81
  3. 3. σ = −3
  4. 4. ts = 0.6667 s
  5. 5. ts = 0.4 s
  6. 6. ts = 1.6 s

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