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)50.5 s2.5

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 5. At t = 0.5 s it reads 2.5. Find the time constant τ.

y(∞) = 5y(0.5) = 2.5
τ = s
2.Easy
t (s)y(t)2010 s8

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 10 s it reads 8. Find the time constant τ.

y(∞) = 20y(10) = 8
τ = s
3.Medium
t (s)y(t)3tp​ = ?

A system has the transfer function G(s) = 36/(s² + s + 12) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 36/(s² + s + 12)
tp = s
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 54/(s² + 2s + 27) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 54/(s² + 2s + 27)
σ =
5.Hard
R(s)+300s(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 300/(s(s + 5)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 300/(s(s + 5))
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 15 % overshoot.

G(s) = K/(s(s + 8))%OS = 15 %
K =

Answer key

  1. 1. τ = 0.7213 s
  2. 2. τ = 19.58 s
  3. 3. tp = 0.9165 s
  4. 4. σ = −1
  5. 5. ts = 1.6 s
  6. 6. K = 59.88

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