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)200.5 s8

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 0.5 s it reads 8. Find the time constant τ.

y(∞) = 20y(0.5) = 8
τ = s
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 8/(s + 4) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 8/(s + 4)U = 20
y(∞) =
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 146/(s² + 13s + 73) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 146/(s² + 13s + 73)
tp = s
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 48/(s² + 10s + 48) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 48/(s² + 10s + 48)
ωn = rad/s
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 10 % overshoot.

G(s) = K/(s(s + 6))%OS = 10 %
K =
6.Hard
t (s)y(t)18 %

A second-order system without zeros must have a step response with 8 % overshoot. Find the damping ratio ζ.

%OS = 8 %
ζ =

Answer key

  1. 1. τ = 0.9788 s
  2. 2. y(∞) = 40
  3. 3. tp = 0.5665 s
  4. 4. ωn = 6.928 rad/s
  5. 5. K = 25.75
  6. 6. ζ = 0.6266

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