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)40.5 s1.2

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 4. At t = 0.5 s it reads 1.2. Find the time constant τ.

y(∞) = 4y(0.5) = 1.2
τ = s
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 2.5/(s + 5) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(s + 5)U = 10
y(∞) =
3.Medium
t (s)y(t)2

A system has the transfer function G(s) = 188/(s² + 4s + 94) and receives a unit step input. Find the damping ratio ζ.

G(s) = 188/(s² + 4s + 94)
ζ =
4.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 5/(s² + 3s + 5) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 5/(s² + 3s + 5)
%OS = %
5.Hard
R(s)+260s(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = 260/(s(s + 16)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 260/(s(s + 16))
ts = s
6.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 2 % overshoot.

G(s) = K/(s(s + 8))%OS = 2 %
K =

Answer key

  1. 1. τ = 1.402 s
  2. 2. y(∞) = 5
  3. 3. ζ = 0.2063
  4. 4. %OS = 5.833 %
  5. 5. ts = 0.5 s
  6. 6. K = 26.32

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