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)+11G₁5G₂C(s)1H−

In the block diagram the forward path has the gains G₁ = 11 and G₂ = 5 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 11G₂ = 5H = 1
T =
2.Easy
R(s)+14G₁3G₂C(s)0.05H−

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 = 0.05. Find the overall gain T = C/R.

G₁ = 14G₂ = 3H = 0.05
T =
3.Medium
R(s)+35s + 7G(s)C(s)0.25H−

A plant G(s) = 35/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. A step of size 10 is applied at R. Find the steady-state output css.

G(s) = 35/(s + 7)H = 0.25R = 10
css =
4.Medium
R(s)+6K+1s + 5G(s)C(s)4H₁−−

The plant G(s) = 1/(s + 5) 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 DC gain T(0).

G(s) = 1/(s + 5)H₁ = 4K = 6
T(0) =
5.Hard
R(s)+Kcontroller+D(s)+7s + 9plantC(s)−

A proportional controller K drives the plant G(s) = 7/(s + 9) in a unity negative feedback loop. A disturbance step of size 5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.7778.

G(s) = 7/(s + 9)D = 5css ≤ 0.7778
K =
6.Hard
R(s)+17controller+D(s)+8s + 4plantC(s)−

A proportional controller K = 17 drives the plant G(s) = 8/(s + 4) 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 = 17G(s) = 8/(s + 4)D = 0.5R = 0
css =

Answer key

  1. 1. T = 0.9821
  2. 2. T = 13.55
  3. 3. css = 22.22
  4. 4. T(0) = 0.4
  5. 5. K = 5.143
  6. 6. css = 0.02857

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