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)2010 s6

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 10 s it reads 6. Find the time constant τ.

y(∞) = 20y(10) = 6
τ = s
2.Easy
t (s)y(t)y(∞) = ?

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

G(s) = 1/(4s + 1)U = 1
y(∞) =
3.Medium
t (s)y(t)0.5tp​ = ?

A system has the transfer function G(s) = 5/(s² + 5s + 10) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 5/(s² + 5s + 10)
tp = s
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 15/(s² + 6s + 15) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 15/(s² + 6s + 15)
ωn = rad/s
5.Hard
R(s)+75s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 75/(s(s + 2)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 75/(s(s + 2))
ts = s
6.Hard
R(s)+205s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 205/(s(s + 10)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 205/(s(s + 10))
ts = s

Answer key

  1. 1. τ = 28.04 s
  2. 2. y(∞) = 1
  3. 3. tp = 1.622 s
  4. 4. ωn = 3.873 rad/s
  5. 5. ts = 4 s
  6. 6. ts = 0.8 s

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