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)2t = ?98 %

A first-order system G(s) = 1/(5s + 1) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 98 % of its final value? Find t.

G(s) = 1/(5s + 1)U = 298 %
t = s
2.Easy
+−10 VR = 1 kΩC = 4.7 µFvC​

An uncharged capacitor C = 4.7 µF is charged from a 10 V step source through a resistor R = 1 kΩ. Find the capacitor voltage vC at t = 1.175 ms.

R = 1 kΩC = 4.7 µFV = 10 Vt = 1.175 ms
vC = V
3.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 146/(s² + 9s + 73) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 146/(s² + 9s + 73)
ts = s
4.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 249/(s² + 9s + 83) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 249/(s² + 9s + 83)
%OS = %
5.Hard
R(s)+Ks(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 6)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 6))%OS = 30 %
K =
6.Hard
R(s)+75s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 75/(s(s + 2)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 75/(s(s + 2))
ts = s

Answer key

  1. 1. t = 19.56 s
  2. 2. vC = 2.212 V
  3. 3. ts = 0.8889 s
  4. 4. %OS = 16.79 %
  5. 5. K = 70.28
  6. 6. ts = 4 s

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