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

A first-order system G(s) = 5/(s + 5) receives a step input of size 10 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 5/(s + 5)U = 10

y(∞) =

2.Easy

A step is applied to a first-order process at t = 0. The output starts at 0 and settles at 100. At t = 0.5 s it reads 90. Find the time constant τ.

y(∞) = 100y(0.5) = 90

τ = s

3.Medium

A system has the transfer function G(s) = 17/(s² + 5s + 17) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 17/(s² + 5s + 17)

t_s = s

4.Medium

A system has the transfer function G(s) = 102/(s² + 2s + 34) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 102/(s² + 2s + 34)

t_p = s

5.Hard

A series RLC circuit with R = 40 Ω, L = 100 mH and C = 22 µF is connected to a 5 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the time t_p of the first voltage peak, in ms.

R = 40 ΩL = 100 mHC = 22 µFV = 5 V

t_p = ms

6.Hard

A series RLC circuit with R = 32 Ω, L = 100 mH and C = 100 µF is connected to a 10 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the percent overshoot %OS of the capacitor voltage.

R = 32 ΩL = 100 mHC = 100 µFV = 10 V

%OS = %

Answer key

1. y(∞) = 10
2. τ = 0.2171 s
3. t_s = 1.6 s
4. t_p = 0.5469 s
5. t_p = 4.879 ms
6. %OS = 15.84 %

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