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) = 2.5/(0.2s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 2.5/(0.2s + 1)U = 10
y(∞) =
2.Easy
+−5 VR = 2.2 kΩC = 100 µFvC​

An uncharged capacitor C = 100 µF is charged from a 5 V step source through a resistor R = 2.2 kΩ. How long after closing the switch does the capacitor voltage reach 80 % of its final value? Find t in ms.

R = 2.2 kΩC = 100 µFV = 5 V80 %
t = ms
3.Medium
t (s)y(t)2ts​ = ?

A system has the transfer function G(s) = 124/(s² + 2s + 62) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 124/(s² + 2s + 62)
ts = s
4.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 39.5/(s² + 14s + 79) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 39.5/(s² + 14s + 79)
σ =
5.Hard
t (s)y(t)14.3 %

A second-order system without zeros must have a step response with 4.3 % overshoot. Find the damping ratio ζ.

%OS = 4.3 %
ζ =
6.Hard
t (s)y(t)1tp​ = 1.5 s15 %

The step response of a second-order system without zeros shows 15 % overshoot, and the first peak occurs at t = 1.5 s. Find the natural frequency ωn.

%OS = 15 %tp = 1.5 s
ωn = rad/s

Answer key

  1. 1. y(∞) = 25
  2. 2. t = 354.1 ms
  3. 3. ts = 4 s
  4. 4. σ = −7
  5. 5. ζ = 0.7077
  6. 6. ωn = 2.447 rad/s

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