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)5G₂1G₃++3G₁C(s)

The signal R splits into two parallel blocks G₂ = 5 and G₃ = 1. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 3. Find the overall gain T = C/R.

G₁ = 3G₂ = 5G₃ = 1signs: + G₂, + G₃
T =
2.Easy
R(s)+4GC(s)0.1H+

An amplifier with gain G = 4 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 = 4H = 0.1positive feedback
T =
3.Medium
R(s)+15s + 5G(s)C(s)0.2H−

A plant G(s) = 15/(s + 5) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 15/(s + 5)H = 0.2R = 1
css =
4.Medium
R(s)+39s + 8G(s)C(s)2H−

A plant G(s) = 39/(s + 8) 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) = 39/(s + 8)H = 2
τ = s
5.Hard
R(s)+K(s + 5)(s + 6)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 5)(s + 6)(s + 7)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/((s + 5)(s + 6)(s + 7))unity negative feedback
Kmax =
6.Hard
R(s)+Kcontroller+D(s)+3s + 7plantC(s)−

A proportional controller K drives the plant G(s) = 3/(s + 7) in a unity negative feedback loop. A disturbance step of size 1 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.02143.

G(s) = 3/(s + 7)D = 1css ≤ 0.02143
K =

Answer key

  1. 1. T = 18
  2. 2. T = 6.667
  3. 3. css = 1.875
  4. 4. τ = 0.01163 s
  5. 5. Kmax = 1716
  6. 6. K = 44.33

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