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)10.025 s?

A first-order system G(s) = 10/(s + 20) receives a step input of size 2 at t = 0, starting from rest. Find the output y(0.025) at t = 0.025 s.

G(s) = 10/(s + 20)U = 2t = 0.025 s
y(0.025) =
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 2/(0.5s + 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/(0.5s + 1)U = 5
y(∞) =
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 78/(s² + 9s + 78) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 78/(s² + 9s + 78)
σ =
4.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 30/(s² + 5s + 60) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 30/(s² + 5s + 60)
%OS = %
5.Hard
R(s)+Ks(s + 20)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 20)). Find the gain K that gives a step response with 10 % overshoot.

G(s) = K/(s(s + 20))%OS = 10 %
K =
6.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 20 % overshoot.

G(s) = K/(s(s + 12))%OS = 20 %
K =

Answer key

  1. 1. y(0.025) = 0.3935
  2. 2. y(∞) = 10
  3. 3. σ = −4.5
  4. 4. %OS = 34.26 %
  5. 5. K = 286.2
  6. 6. K = 173.2

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