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) = 0.5/(10s + 1) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 0.5/(10s + 1)U = 10
y(∞) =
2.Easy
t (s)y(t)83 s4.8

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 8. At t = 3 s it reads 4.8. Find the time constant τ.

y(∞) = 8y(3) = 4.8
τ = s
3.Medium
t (s)y(t)0.5

A system has the transfer function G(s) = 43.5/(s² + 13s + 87) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 43.5/(s² + 13s + 87)
σ =
4.Medium
t (s)y(t)2

A system has the transfer function G(s) = 196/(s² + 10s + 98) and receives a unit step input. The poles are s = σ ± jωd. Find the real part σ.

G(s) = 196/(s² + 10s + 98)
σ =
5.Hard
R(s)+Ks(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 12)). Find the gain K that gives a step response with 5 % overshoot.

G(s) = K/(s(s + 12))%OS = 5 %
K =
6.Hard
R(s)+80s(s + 12)G(s)C(s)−

A unity negative feedback loop has G(s) = 80/(s(s + 12)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 80/(s(s + 12))
ts = s

Answer key

  1. 1. y(∞) = 5
  2. 2. τ = 3.274 s
  3. 3. σ = −6.5
  4. 4. σ = −5
  5. 5. K = 75.59
  6. 6. ts = 0.6667 s

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