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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
t (s)y(t)80.8 s?

A first-order system G(s) = 4/(4s + 1) receives a step input of size 2 at t = 0, starting from rest. Find the output y(0.8) at t = 0.8 s.

G(s) = 4/(4s + 1)U = 2t = 0.8 s
y(0.8) =
2.Easy
t (s)y(t)8t = ?80 %

A first-order system G(s) = 4/(1s + 1) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 80 % of its final value? Find t.

G(s) = 4/(1s + 1)U = 280 %
t = s
3.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 70/(s² + 12s + 70) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 70/(s² + 12s + 70)
%OS = %
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 90/(s² + 15s + 90) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 90/(s² + 15s + 90)
σ =
5.Hard
R(s)+Ks(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 8)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 8))%OS = 30 %
K =
6.Hard
R(s)+170s(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = 170/(s(s + 16)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 170/(s(s + 16))
ts = s

Answer key

  1. 1. y(0.8) = 1.45
  2. 2. t = 1.609 s
  3. 3. %OS = 3.945 %
  4. 4. σ = −7.5
  5. 5. K = 124.9
  6. 6. ts = 0.5 s

Full step-by-step solutions: practise this topic on examproblems.com.