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)102 s?

A first-order system G(s) = 0.25/(s + 0.5) receives a step input of size 20 at t = 0, starting from rest. Find the output y(2) at t = 2 s.

G(s) = 0.25/(s + 0.5)U = 20t = 2 s
y(2) =
2.Easy
+−24 VR = 10 kΩC = 47 µFvC​

An uncharged capacitor C = 47 µF is charged from a 24 V step source through a resistor R = 10 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 10 kΩC = 47 µFV = 24 V
tr = ms
3.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 18.5/(s² + 7s + 37) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 18.5/(s² + 7s + 37)
%OS = %
4.Medium
t (s)y(t)3tp​ = ?

A system has the transfer function G(s) = 240/(s² + 4s + 80) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 240/(s² + 4s + 80)
tp = s
5.Hard
R(s)+125s(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 125/(s(s + 4)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 125/(s(s + 4))
ts = s
6.Hard
R(s)+Ks(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 16)). Find the gain K that gives a step response with 10 % overshoot.

G(s) = K/(s(s + 16))%OS = 10 %
K =

Answer key

  1. 1. y(2) = 6.321
  2. 2. tr = 1033 ms
  3. 3. %OS = 10.97 %
  4. 4. tp = 0.3604 s
  5. 5. ts = 2 s
  6. 6. K = 183.1

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