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) = 10/(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) = 10/(2s + 1)U = 10
y(∞) =
2.Easy
t (s)y(t)25 s1.6

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 2. At t = 5 s it reads 1.6. Find the time constant τ.

y(∞) = 2y(5) = 1.6
τ = s
3.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 126/(s² + 4s + 42) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 126/(s² + 4s + 42)
%OS = %
4.Medium
t (s)y(t)1

A system has the transfer function G(s) = 63/(s² + 10s + 63) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 63/(s² + 10s + 63)
σ =
5.Hard
R(s)+195s(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 195/(s(s + 6)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 195/(s(s + 6))
ts = s
6.Hard
R(s)+220s(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = 220/(s(s + 12)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 220/(s(s + 12))
ts = s

Answer key

  1. 1. y(∞) = 100
  2. 2. τ = 3.107 s
  3. 3. %OS = 36.09 %
  4. 4. σ = −5
  5. 5. ts = 1.333 s
  6. 6. ts = 0.6667 s

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