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) = 15/(s + 5) receives a step input of size 5 at t = 0, starting from rest. How long does the output take to reach 95 % of its final value? Find t.

G(s) = 15/(s + 5)U = 595 %

t = s

2.Easy

An uncharged capacitor C = 1 µF is charged from a 24 V step source through a resistor R = 22 kΩ. Find the 10–90 % rise time t_r of the capacitor voltage, in ms.

R = 22 kΩC = 1 µFV = 24 V

t_r = ms

3.Medium

A system has the transfer function G(s) = 112/(s² + 9s + 56) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 112/(s² + 9s + 56)

%OS = %

4.Medium

A system has the transfer function G(s) = 88/(s² + 13s + 88) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 88/(s² + 13s + 88)

σ =

5.Hard

A series RLC circuit with R = 54 Ω, L = 200 mH and C = 100 µF is connected to a 24 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 = 54 ΩL = 200 mHC = 100 µFV = 24 V

%OS = %

6.Hard

A series RLC circuit with R = 57 Ω, L = 50 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 = 57 ΩL = 50 mHC = 22 µFV = 5 V

t_p = ms

Answer key

1. t = 0.5991 s
2. t_r = 48.34 ms
3. %OS = 9.4 %
4. σ = −6.5
5. %OS = 9.262 %
6. t_p = 4.11 ms

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