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 step is applied to a first-order process at t = 0. The output starts at 0 and settles at 100. At t = 1 s it reads 70. Find the time constant τ.

y(∞) = 100y(1) = 70

τ = s

2.Easy

A first-order system G(s) = 20/(s + 20) receives a step input of size 2 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 20/(s + 20)U = 2

y(∞) =

3.Medium

A system has the transfer function G(s) = 40/(s² + 7s + 20) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 40/(s² + 7s + 20)

t_s = s

4.Medium

A system has the transfer function G(s) = 99/(s² + 13s + 99) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 99/(s² + 13s + 99)

σ =

5.Hard

A second-order system without zeros must have a step response with 40 % overshoot. Find the damping ratio ζ.

%OS = 40 %

ζ =

6.Hard

A series RLC circuit with R = 179 Ω, L = 500 mH and C = 10 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage v_C,max.

R = 179 ΩL = 500 mHC = 10 µFV = 12 V

v_C,max = V

Answer key

1. τ = 0.8306 s
2. y(∞) = 2
3. t_s = 1.143 s
4. σ = −6.5
5. ζ = 0.28
6. v_C,max = 15.04 V

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