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)2.50.2 s?

A first-order system G(s) = 0.5/(s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the output y(0.2) at t = 0.2 s.

G(s) = 0.5/(s + 1)U = 5t = 0.2 s
y(0.2) =
2.Easy
t (s)y(t)205 s10

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 5 s it reads 10. Find the time constant τ.

y(∞) = 20y(5) = 10
τ = s
3.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 77/(s² + 6s + 77) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 77/(s² + 6s + 77)
%OS = %
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 64/(s² + 9s + 32) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 64/(s² + 9s + 32)
%OS = %
5.Hard
R(s)+Ks(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 6)). Find the gain K that gives a step response with 2 % overshoot.

G(s) = K/(s(s + 6))%OS = 2 %
K =
6.Hard
R(s)+Ks(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 6)). Find the gain K that gives a step response with 5 % overshoot.

G(s) = K/(s(s + 6))%OS = 5 %
K =

Answer key

  1. 1. y(0.2) = 0.4532
  2. 2. τ = 7.213 s
  3. 3. %OS = 31.89 %
  4. 4. %OS = 1.618 %
  5. 5. K = 14.8
  6. 6. K = 18.9

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