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 2. At t = 5 s it reads 1. Find the time constant τ.

y(∞) = 2y(5) = 1

τ = s

2.Easy

A first-order system G(s) = 1/(5s + 1) receives a step input of size 20 at t = 0, starting from rest. Find the final value y(∞) of the output.

G(s) = 1/(5s + 1)U = 20

y(∞) =

3.Medium

A system has the transfer function G(s) = 37/(s² + 4s + 37) and receives a unit step input. Find the peak time t_p of the step response.

G(s) = 37/(s² + 4s + 37)

t_p = s

4.Medium

A system has the transfer function G(s) = 63/(s² + 7s + 21) and receives a unit step input. Find the percent overshoot %OS of the step response.

G(s) = 63/(s² + 7s + 21)

%OS = %

5.Hard

A unity negative feedback loop has G(s) = K/(s(s + 5)). Find the gain K that gives a step response with 30 % overshoot.

G(s) = K/(s(s + 5))%OS = 30 %

K =

6.Hard

A unity negative feedback loop has G(s) = 280/(s(s + 10)). Find the 2 % settling time t_s of the closed-loop step response, using t_s ≈ 4/(ζωₙ).

G(s) = 280/(s(s + 10))

t_s = s

Answer key

1. τ = 7.213 s
2. y(∞) = 20
3. t_p = 0.5469 s
4. %OS = 2.43 %
5. K = 48.8
6. t_s = 0.8 s

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