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)53 s2.5

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 5. At t = 3 s it reads 2.5. Find the time constant τ.

y(∞) = 5y(3) = 2.5
τ = s
2.Easy
t (s)y(t)y(∞) = ?

A first-order system G(s) = 10/(0.8s + 1) receives a step input of size 1 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 10/(0.8s + 1)U = 1
y(∞) =
3.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 44/(s² + 5s + 44) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 44/(s² + 5s + 44)
ts = s
4.Medium
t (s)y(t)3?

A system has the transfer function G(s) = 117/(s² + 9s + 39) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 117/(s² + 9s + 39)
%OS = %
5.Hard
R(s)+Ks(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 4)). Find the gain K that gives a step response with 15 % overshoot.

G(s) = K/(s(s + 4))%OS = 15 %
K =
6.Hard
t (s)y(t)1tp​ = 1 s12 %

The step response of a second-order system without zeros shows 12 % overshoot, and the first peak occurs at t = 1 s. Find the natural frequency ωn.

%OS = 12 %tp = 1 s
ωn = rad/s

Answer key

  1. 1. τ = 4.328 s
  2. 2. y(∞) = 10
  3. 3. ts = 1.6 s
  4. 4. %OS = 3.82 %
  5. 5. K = 14.97
  6. 6. ωn = 3.79 rad/s

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