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)12.5t = ?75 %

A first-order system G(s) = 2.5/(0.5s + 1) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 75 % of its final value? Find t.

G(s) = 2.5/(0.5s + 1)U = 575 %
t = s
2.Easy
t (s)y(t)y(∞) = ?

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

G(s) = 1/(s + 0.5)U = 5
y(∞) =
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 42/(s² + 7s + 42) and receives a unit step input. Find the damping ratio ζ.

G(s) = 42/(s² + 7s + 42)
ζ =
4.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 102/(s² + 5s + 51) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 102/(s² + 5s + 51)
ts = s
5.Hard
t (s)y(t)110 %

A second-order system without zeros must have a step response with 10 % overshoot. Find the damping ratio ζ.

%OS = 10 %
ζ =
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 15 % overshoot.

G(s) = K/(s(s + 6))%OS = 15 %
K =

Answer key

  1. 1. t = 0.6931 s
  2. 2. y(∞) = 10
  3. 3. ζ = 0.5401
  4. 4. ts = 1.6 s
  5. 5. ζ = 0.5912
  6. 6. K = 33.68

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