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) = 2/(2s + 1) receives a step input of size 5 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2/(2s + 1)U = 5
y(∞) =
2.Easy
+−12 VR = 22 kΩC = 10 µFvC​

An uncharged capacitor C = 10 µF is charged from a 12 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 = 10 µFV = 12 V
tr = ms
3.Medium
t (s)y(t)1

A system has the transfer function G(s) = 35/(s² + 2s + 35) and receives a unit step input. Find the damping ratio ζ.

G(s) = 35/(s² + 2s + 35)
ζ =
4.Medium
t (s)y(t)2?

A system has the transfer function G(s) = 152/(s² + 5s + 76) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 152/(s² + 5s + 76)
%OS = %
5.Hard
R(s)+80s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 80/(s(s + 10)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 80/(s(s + 10))
ts = s
6.Hard
t (s)y(t)125 %

A second-order system without zeros must have a step response with 25 % overshoot. Find the damping ratio ζ.

%OS = 25 %
ζ =

Answer key

  1. 1. y(∞) = 10
  2. 2. tr = 483.4 ms
  3. 3. ζ = 0.169
  4. 4. %OS = 39.05 %
  5. 5. ts = 0.8 s
  6. 6. ζ = 0.4037

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