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)+14G₁3G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 14 and G₂ = 3 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 14G₂ = 3H = 0.1
T =
2.Easy
R(s)+19G₁1G₂C(s)1H−

In the block diagram the forward path has the gains G₁ = 19 and G₂ = 1 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 19G₂ = 1H = 1
T =
3.Medium
R(s)+18s + 10G(s)C(s)2H−

A plant G(s) = 18/(s + 10) is controlled in a negative feedback loop whose sensor has the gain H = 2. Find the time constant τ of the closed loop.

G(s) = 18/(s + 10)H = 2
τ = s
4.Medium
R(s)+3K+7s + 3G(s)C(s)1H₁−−

The plant G(s) = 7/(s + 3) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 3 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 7/(s + 3)H₁ = 1K = 3
p =
5.Hard
R(s)+Kcontroller+D(s)+9s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 9/(s + 4) in a unity negative feedback loop. A disturbance step of size 2 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.045.

G(s) = 9/(s + 4)D = 2css ≤ 0.045
K =
6.Hard
R(s)+9controller+D(s)+5s + 9plantC(s)−

A proportional controller K = 9 drives the plant G(s) = 5/(s + 9) 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 1 and a disturbance step of size 5 are applied together. Find the steady-state output css.

K = 9G(s) = 5/(s + 9)D = 5R = 1
css =

Answer key

  1. 1. T = 8.077
  2. 2. T = 0.95
  3. 3. τ = 0.02174 s
  4. 4. p = −31
  5. 5. K = 44
  6. 6. css = 1.296

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