Block diagrams worksheet with answers

Free printable Block diagrams worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise 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
R(s)+7s + 1G(s)C(s)−

A plant G(s) = 7/(s + 1) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 7/(s + 1)unity negative feedback
T(0) =
2.Easy
R(s)+18GC(s)0.02H+

An amplifier with gain G = 18 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 18H = 0.02positive feedback
T =
3.Medium
R(s)+4(s + 1)(s + 2)(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 4(s + 1)/((s + 2)(s + 5)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 4(s + 1)/((s + 2)(s + 5))R = 5
ess =
4.Medium
R(s)+46s(s + 3)G(s)C(s)−

A unity negative feedback loop has G(s) = 46/(s(s + 3)). The reference is a ramp r(t) = 2·t. Find the steady-state error ess.

G(s) = 46/(s(s + 3))r(t) = 2·t
ess =
5.Hard
R(s)+27controller+D(s)+1s + 8plantC(s)−

A proportional controller K = 27 drives the plant G(s) = 1/(s + 8) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 5 and a disturbance step of size 2 are applied together. Find the steady-state output css.

K = 27G(s) = 1/(s + 8)D = 2R = 5
css =
6.Hard
R(s)+K(s + 4)(s + 6)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 4)(s + 6)(s + 8)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/((s + 4)(s + 6)(s + 8))unity negative feedback
ω = rad/s

Answer key

  1. 1. T(0) = 0.875
  2. 2. T = 28.13
  3. 3. ess = 3.571
  4. 4. ess = 0.1304
  5. 5. css = 3.914
  6. 6. ω = 10.2 rad/s

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