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)5010 s45

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 50. At t = 10 s it reads 45. Find the time constant τ.

y(∞) = 50y(10) = 45
τ = s
2.Easy
+−5 VR = 22 kΩC = 4.7 µFvC​

An uncharged capacitor C = 4.7 µF is charged from a 5 V step source through a resistor R = 22 kΩ. Find the capacitor voltage vC at t = 51.7 ms.

R = 22 kΩC = 4.7 µFV = 5 Vt = 51.7 ms
vC = V
3.Medium
t (s)y(t)0.5?

A system has the transfer function G(s) = 46/(s² + 6s + 92) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 46/(s² + 6s + 92)
%OS = %
4.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 70/(s² + 7s + 35) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 70/(s² + 7s + 35)
tp = s
5.Hard
+−12 VR = 8 ΩL = 20 mHC = 47 µFvC​

A series RLC circuit with R = 8 Ω, L = 20 mH and C = 47 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time tp of the first voltage peak, in ms.

R = 8 ΩL = 20 mHC = 47 µFV = 12 V
tp = ms
6.Hard
R(s)+230s(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = 230/(s(s + 16)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 230/(s(s + 16))
ts = s

Answer key

  1. 1. τ = 4.343 s
  2. 2. vC = 1.967 V
  3. 3. %OS = 35.54 %
  4. 4. tp = 0.6587 s
  5. 5. tp = 3.105 ms
  6. 6. ts = 0.5 s

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