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
+−24 VR = 22 kΩC = 1 µFvC​

An uncharged capacitor C = 1 µF is charged from a 24 V step source through a resistor R = 22 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 22 kΩC = 1 µFV = 24 V
tr = ms
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 30/(s + 10) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 30/(s + 10)U = 20
y(∞) =
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 46/(s² + 5s + 23) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 46/(s² + 5s + 23)
tp = s
4.Medium
t (s)y(t)1tp​ = ?

A system has the transfer function G(s) = 52/(s² + 6s + 52) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 52/(s² + 6s + 52)
tp = s
5.Hard
+−24 VR = 25 ΩL = 10 mHC = 10 µFvC​

A series RLC circuit with R = 25 Ω, L = 10 mH and C = 10 µF is connected to a 24 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the undamped natural frequency ωn in rad/s.

R = 25 ΩL = 10 mHC = 10 µFV = 24 V
ωn = rad/s
6.Hard
R(s)+185s(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = 185/(s(s + 12)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 185/(s(s + 12))
ts = s

Answer key

  1. 1. tr = 48.34 ms
  2. 2. y(∞) = 60
  3. 3. tp = 0.7676 s
  4. 4. tp = 0.4791 s
  5. 5. ωn = 3162 rad/s
  6. 6. ts = 0.6667 s

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