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)4G₂10G₃+−10G₁C(s)

The signal R splits into two parallel blocks G₂ = 4 and G₃ = 10. 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 = 4G₃ = 10signs: + G₂, − G₃
T =
2.Easy
R(s)+12GC(s)0.02H+

An amplifier with gain G = 12 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 = 12H = 0.02positive feedback
T =
3.Medium
R(s)+6K+10s + 7G(s)C(s)4H₁−−

The plant G(s) = 10/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 6 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 10/(s + 7)H₁ = 4K = 6
p =
4.Medium
R(s)+11K+9s + 4G(s)C(s)5H₁−−

The plant G(s) = 9/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 11 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 9/(s + 4)H₁ = 5K = 11
p =
5.Hard
R(s)+2s + 1G₁+1s + 7G₂C(s)4H₁−0.1H₂−

Reduce the block diagram with G₁ = 2/(s + 1), G₂ = 1/(s + 7), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 2/(s + 1)G₂ = 1/(s + 7)H₁ = 4H₂ = 0.1
T(0) =
6.Hard
R(s)+10controller+D(s)+3s + 10plantC(s)−

A proportional controller K = 10 drives the plant G(s) = 3/(s + 10) 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 0.5 is applied. Find the steady-state output css.

K = 10G(s) = 3/(s + 10)D = 0.5R = 0
css =

Answer key

  1. 1. T = −60
  2. 2. T = 15.79
  3. 3. p = −107
  4. 4. p = −148
  5. 5. T(0) = 0.1786
  6. 6. css = 0.0375

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