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)202 s?

A first-order system G(s) = 10/(4s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the output y(2) at t = 2 s.

G(s) = 10/(4s + 1)U = 2t = 2 s
y(2) =
2.Easy
t (s)y(t)y(∞) = ?

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

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

A system has the transfer function G(s) = 12/(s² + s + 12) and receives a unit step input. Find the damping ratio ζ.

G(s) = 12/(s² + s + 12)
ζ =
4.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 98/(s² + 10s + 49) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 98/(s² + 10s + 49)
tp = s
5.Hard
t (s)y(t)1tp​ = 2 s8 %

The step response of a second-order system without zeros shows 8 % overshoot, and the first peak occurs at t = 2 s. Find the natural frequency ωn.

%OS = 8 %tp = 2 s
ωn = rad/s
6.Hard
R(s)+145s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 145/(s(s + 10)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 145/(s(s + 10))
ts = s

Answer key

  1. 1. y(2) = 7.869
  2. 2. y(∞) = 12.5
  3. 3. ζ = 0.1443
  4. 4. tp = 0.6413 s
  5. 5. ωn = 2.015 rad/s
  6. 6. ts = 0.8 s

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