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)+3GC(s)0.1H+

An amplifier with gain G = 3 has positive feedback through a path with gain H = 0.1 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 3H = 0.1positive feedback
T =
2.Easy
R(s)+6GC(s)0.05H+

An amplifier with gain G = 6 has positive feedback through a path with gain H = 0.05 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 6H = 0.05positive feedback
T =
3.Medium
R(s)+14K+5s + 2G(s)C(s)0.5H₁−−

The plant G(s) = 5/(s + 2) has an inner (minor) negative feedback loop with gain H₁ = 0.5. A controller gain K = 14 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 5/(s + 2)H₁ = 0.5K = 14
p =
4.Medium
R(s)+10s + 6G(s)C(s)2H−

A plant G(s) = 10/(s + 6) 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) = 10/(s + 6)H = 2
τ = s
5.Hard
R(s)+28controller+D(s)+8s + 5plantC(s)−

A proportional controller K = 28 drives the plant G(s) = 8/(s + 5) 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 5 is applied. Find the steady-state output css.

K = 28G(s) = 8/(s + 5)D = 5R = 0
css =
6.Hard
R(s)+10s(s + 5)G(s)C(s)1H−

The plant G(s) = 10/(s(s + 5)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 10/(s(s + 5))H = 1
σ =

Answer key

  1. 1. T = 4.286
  2. 2. T = 8.571
  3. 3. p = −74.5
  4. 4. τ = 0.03846 s
  5. 5. css = 0.1747
  6. 6. σ = −2.5

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