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)2G₂8G₃+−10G₁C(s)

The signal R splits into two parallel blocks G₂ = 2 and G₃ = 8. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 10. Find the overall gain T = C/R.

G₁ = 10G₂ = 2G₃ = 8signs: + G₂, − G₃
T =
2.Easy
R(s)+7GC(s)0.1H+

An amplifier with gain G = 7 has positive feedback through a path with gain H = 0.1 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 7H = 0.1positive feedback
T =
3.Medium
R(s)+30s + 8G(s)C(s)0.2H−

A plant G(s) = 30/(s + 8) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. A step of size 24 is applied at R. Find the steady-state output css.

G(s) = 30/(s + 8)H = 0.2R = 24
css =
4.Medium
R(s)+14K+3s + 2G(s)C(s)4H₁−−

The plant G(s) = 3/(s + 2) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 14 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 3/(s + 2)H₁ = 4K = 14
p =
5.Hard
R(s)+9controller+D(s)+9s + 3plantC(s)−

A proportional controller K = 9 drives the plant G(s) = 9/(s + 3) 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 = 9G(s) = 9/(s + 3)D = 2R = 5
css =
6.Hard
R(s)+19controller+D(s)+10s + 7plantC(s)−

A proportional controller K = 19 drives the plant G(s) = 10/(s + 7) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). With R = 0, a disturbance step of size 1 is applied. Find the steady-state output css.

K = 19G(s) = 10/(s + 7)D = 1R = 0
css =

Answer key

  1. 1. T = −60
  2. 2. T = 23.33
  3. 3. css = 51.43
  4. 4. p = −56
  5. 5. css = 5.036
  6. 6. css = 0.05076

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