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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.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(∞) =

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) = 20.5/(s² + 4s + 41) and receives a unit step input. Find the 2 % settling time t_s of the step response, using t_s ≈ 4/(ζωₙ).

G(s) = 20.5/(s² + 4s + 41)

t_s = s

4.Medium

A system has the transfer function G(s) = 93/(s² + 3s + 93) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 93/(s² + 3s + 93)

t_p = s

5.Hard

A series RLC circuit with R = 18 Ω, L = 50 mH and C = 100 µF is connected to a 12 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 = 18 ΩL = 50 mHC = 100 µFV = 12 V

t_p = ms

6.Hard

A series RLC circuit with R = 60 Ω, L = 100 mH and C = 10 µF is connected to a 5 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 = 60 ΩL = 100 mHC = 10 µFV = 5 V

%OS = %

Answer key

1. y(∞) = 2
2. τ = 0.2171 s
3. t_s = 2 s
4. t_p = 0.3298 s
5. t_p = 7.674 ms
6. %OS = 37.23 %

Full step-by-step solutions: practise this topic on examproblems.com.