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)y(∞) = ?

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

G(s) = 5/(0.5s + 1)U = 5
y(∞) =
2.Easy
t (s)y(t)505 s15

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 50. At t = 5 s it reads 15. Find the time constant τ.

y(∞) = 50y(5) = 15
τ = s
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 108/(s² + 3s + 54) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 108/(s² + 3s + 54)
tp = s
4.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 86/(s² + 6s + 43) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 86/(s² + 6s + 43)
ts = s
5.Hard
+−24 VR = 57 ΩL = 10 mHC = 2 µFvC​

A series RLC circuit with R = 57 Ω, L = 10 mH and C = 2 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage vC,max.

R = 57 ΩL = 10 mHC = 2 µFV = 24 V
vC,max = V
6.Hard
R(s)+Ks(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 10)). Find the gain K that gives a step response with 10 % overshoot.

G(s) = K/(s(s + 10))%OS = 10 %
K =

Answer key

  1. 1. y(∞) = 25
  2. 2. τ = 14.02 s
  3. 3. tp = 0.4367 s
  4. 4. ts = 1.333 s
  5. 5. vC,max = 30.02 V
  6. 6. K = 71.54

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