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) = 20/(s + 10) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 20/(s + 10)U = 5
y(∞) =
2.Easy
+−9 VR = 4.7 kΩC = 2.2 µFvC​

An uncharged capacitor C = 2.2 µF is charged from a 9 V step source through a resistor R = 4.7 kΩ. Find the capacitor voltage vC at t = 15.51 ms.

R = 4.7 kΩC = 2.2 µFV = 9 Vt = 15.51 ms
vC = V
3.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 46/(s² + 7s + 23) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 46/(s² + 7s + 23)
ts = s
4.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 135/(s² + 4s + 45) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 135/(s² + 4s + 45)
%OS = %
5.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 2 % overshoot.

G(s) = K/(s(s + 12))%OS = 2 %
K =
6.Hard
R(s)+245s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 245/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 245/(s(s + 8))
ts = s

Answer key

  1. 1. y(∞) = 10
  2. 2. vC = 6.992 V
  3. 3. ts = 1.143 s
  4. 4. %OS = 37.48 %
  5. 5. K = 59.22
  6. 6. ts = 1 s

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