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) = 5/(1s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 5/(1s + 1)U = 20
y(∞) =
2.Easy
+−24 VR = 100 kΩC = 10 µFvC​

An uncharged capacitor C = 10 µF is charged from a 24 V step source through a resistor R = 100 kΩ. Find the 10–90 % rise time tr of the capacitor voltage, in ms.

R = 100 kΩC = 10 µFV = 24 V
tr = ms
3.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 18/(s² + 4s + 9) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 18/(s² + 4s + 9)
%OS = %
4.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 20.5/(s² + 5s + 41) and receives a unit step input. Find the natural frequency ωn in rad/s.

G(s) = 20.5/(s² + 5s + 41)
ωn = rad/s
5.Hard
+−10 VR = 10 ΩL = 10 mHC = 100 µFvC​

A series RLC circuit with R = 10 Ω, L = 10 mH and C = 100 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the percent overshoot %OS of the capacitor voltage.

R = 10 ΩL = 10 mHC = 100 µFV = 10 V
%OS = %
6.Hard
R(s)+150s(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = 150/(s(s + 12)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 150/(s(s + 12))
ts = s

Answer key

  1. 1. y(∞) = 100
  2. 2. tr = 2197 ms
  3. 3. %OS = 6.021 %
  4. 4. ωn = 6.403 rad/s
  5. 5. %OS = 16.3 %
  6. 6. ts = 0.6667 s

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