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)11G₂2G₃++9G₁C(s)

The signal R splits into two parallel blocks G₂ = 11 and G₃ = 2. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 9. Find the overall gain T = C/R.

G₁ = 9G₂ = 11G₃ = 2signs: + G₂, + G₃
T =
2.Easy
R(s)9G₂6G₃+−9G₁C(s)

The signal R splits into two parallel blocks G₂ = 9 and G₃ = 6. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 9. Find the overall gain T = C/R.

G₁ = 9G₂ = 9G₃ = 6signs: + G₂, − G₃
T =
3.Medium
R(s)+8K+2s + 4G(s)C(s)1H₁−−

The plant G(s) = 2/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 8 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 2/(s + 4)H₁ = 1K = 8
T(0) =
4.Medium
R(s)+48s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 48/(s(s + 10)). The reference is a ramp r(t) = 1·t. Find the steady-state error ess.

G(s) = 48/(s(s + 10))r(t) = 1·t
ess =
5.Hard
R(s)+Kcontroller+D(s)+4s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 4/(s + 4) in a unity negative feedback loop. A disturbance step of size 10 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.2.

G(s) = 4/(s + 4)D = 10css ≤ 0.2
K =
6.Hard
R(s)+54s(s + 10)G(s)C(s)1H−

The plant G(s) = 54/(s(s + 10)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 54/(s(s + 10))H = 1
ωd = rad/s

Answer key

  1. 1. T = 117
  2. 2. T = 27
  3. 3. T(0) = 0.7273
  4. 4. ess = 0.2083
  5. 5. K = 49
  6. 6. ωd = 5.385 rad/s

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