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)+17GC(s)0.01H+

An amplifier with gain G = 17 has positive feedback through a path with gain H = 0.01 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 17H = 0.01positive feedback
T =
2.Easy
R(s)8G₂6G₃++8G₁C(s)

The signal R splits into two parallel blocks G₂ = 8 and G₃ = 6. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 8. Find the overall gain T = C/R.

G₁ = 8G₂ = 8G₃ = 6signs: + G₂, + G₃
T =
3.Medium
R(s)+58s(s + 7)G(s)C(s)−

A unity negative feedback loop has G(s) = 58/(s(s + 7)). The reference is a ramp r(t) = 1·t. Find the steady-state error ess.

G(s) = 58/(s(s + 7))r(t) = 1·t
ess =
4.Medium
R(s)+13K+7s + 8G(s)C(s)5H₁−−

The plant G(s) = 7/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 13 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 7/(s + 8)H₁ = 5K = 13
p =
5.Hard
R(s)+Kcontroller+D(s)+9s + 6plantC(s)−

A proportional controller K drives the plant G(s) = 9/(s + 6) in a unity negative feedback loop. A disturbance step of size 0.5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.075.

G(s) = 9/(s + 6)D = 0.5css ≤ 0.075
K =
6.Hard
R(s)+10controller+D(s)+3s + 1plantC(s)−

A proportional controller K = 10 drives the plant G(s) = 3/(s + 1) 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 10 is applied. Find the steady-state output css.

K = 10G(s) = 3/(s + 1)D = 10R = 0
css =

Answer key

  1. 1. T = 20.48
  2. 2. T = 112
  3. 3. ess = 0.1207
  4. 4. p = −134
  5. 5. K = 6
  6. 6. css = 0.9677

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