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)503 s40

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 50. At t = 3 s it reads 40. Find the time constant τ.

y(∞) = 50y(3) = 40
τ = s
2.Easy
t (s)y(t)205 s6

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 20. At t = 5 s it reads 6. Find the time constant τ.

y(∞) = 20y(5) = 6
τ = s
3.Medium
t (s)y(t)2tp​ = ?

A system has the transfer function G(s) = 102/(s² + 10s + 51) and receives a unit step input. Find the peak time tp of the step response.

G(s) = 102/(s² + 10s + 51)
tp = s
4.Medium
t (s)y(t)1ts​ = ?

A system has the transfer function G(s) = 90/(s² + 4s + 90) and receives a unit step input. Find the 2 % settling time ts of the step response, using ts ≈ 4/(ζωₙ).

G(s) = 90/(s² + 4s + 90)
ts = s
5.Hard
R(s)+Ks(s + 16)G(s)C(s)−

A unity negative feedback loop has G(s) = K/(s(s + 16)). Find the gain K that gives a step response with 2 % overshoot.

G(s) = K/(s(s + 16))%OS = 2 %
K =
6.Hard
R(s)+280s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 280/(s(s + 8)). Find the 2 % settling time ts of the closed-loop step response, using ts ≈ 4/(ζωₙ).

G(s) = 280/(s(s + 8))
ts = s

Answer key

  1. 1. τ = 1.864 s
  2. 2. τ = 14.02 s
  3. 3. tp = 0.6161 s
  4. 4. ts = 2 s
  5. 5. K = 105.3
  6. 6. ts = 1 s

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