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)42 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 = 2 s it reads 1.2. Find the time constant τ.

y(∞) = 4y(2) = 1.2
τ = s
2.Easy
t (s)y(t)5t = ?50 %

A first-order system G(s) = 1/(0.2s + 1) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 50 % of its final value? Find t.

G(s) = 1/(0.2s + 1)U = 550 %
t = s
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 76/(s² + 3s + 76) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 76/(s² + 3s + 76)
σ =
4.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 21/(s² + 8s + 42) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 21/(s² + 8s + 42)
%OS = %
5.Hard
R(s)+240s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 240/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 240/(s(s + 8))
ts = s
6.Hard
R(s)+155s(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 155/(s(s + 6)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 155/(s(s + 6))
ts = s

Answer key

  1. 1. τ = 5.607 s
  2. 2. t = 0.1386 s
  3. 3. σ = −1.5
  4. 4. %OS = 8.505 %
  5. 5. ts = 1 s
  6. 6. ts = 1.333 s

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