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
+−9 VR = 100 kΩC = 10 µFvC​

An uncharged capacitor C = 10 µF is charged from a 9 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 = 9 V
tr = ms
2.Easy
t (s)y(t)10t = ?98 %

A first-order system G(s) = 20/(s + 4) receives a step input of size 2 at t = 0, starting from rest. How long does the output take to reach 98 % of its final value? Find t.

G(s) = 20/(s + 4)U = 298 %
t = s
3.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 36/(s² + 2s + 36) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 36/(s² + 2s + 36)
ts = s
4.Medium
t (s)y(t)1?

A system has the transfer function G(s) = 59/(s² + 9s + 59) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 59/(s² + 9s + 59)
%OS = %
5.Hard
t (s)y(t)12 %

A second-order system without zeros must have a step response with 2 % overshoot. Find the damping ratio ζ.

%OS = 2 %
ζ =
6.Hard
R(s)+190s(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 190/(s(s + 4)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 190/(s(s + 4))
ts = s

Answer key

  1. 1. tr = 2197 ms
  2. 2. t = 0.978 s
  3. 3. ts = 4 s
  4. 4. %OS = 10.32 %
  5. 5. ζ = 0.7797
  6. 6. ts = 2 s

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