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
+−10 VR = 2.2 kΩC = 100 µFvC​

An uncharged capacitor C = 100 µF is charged from a 10 V step source through a resistor R = 2.2 kΩ. How long after closing the switch does the capacitor voltage reach 90 % of its final value? Find t in ms.

R = 2.2 kΩC = 100 µFV = 10 V90 %
t = ms
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 40/(s + 20) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 40/(s + 20)U = 20
y(∞) =
3.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 23/(s² + 6s + 23) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 23/(s² + 6s + 23)
tp = s
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 96/(s² + 16s + 96) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 96/(s² + 16s + 96)
σ =
5.Hard
R(s)+30s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 30/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 30/(s(s + 8))
ts = s
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 25 % overshoot.

G(s) = K/(s(s + 10))%OS = 25 %
K =

Answer key

  1. 1. t = 506.6 ms
  2. 2. y(∞) = 40
  3. 3. tp = 0.8396 s
  4. 4. σ = −8
  5. 5. ts = 1 s
  6. 6. K = 153.4

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