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)5G₂7G₃+−8G₁C(s)

The signal R splits into two parallel blocks G₂ = 5 and G₃ = 7. 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 = 5G₃ = 7signs: + G₂, − G₃
T =
2.Easy
R(s)4G₂9G₃++5G₁C(s)

The signal R splits into two parallel blocks G₂ = 4 and G₃ = 9. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 5. Find the overall gain T = C/R.

G₁ = 5G₂ = 4G₃ = 9signs: + G₂, + G₃
T =
3.Medium
R(s)+K(s + 2)(s + 5)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 5)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).

G(s) = K/((s + 2)(s + 5))unity negative feedback
K =
4.Medium
R(s)+3K+9s + 7G(s)C(s)0.5H₁−−

The plant G(s) = 9/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 0.5. A controller gain K = 3 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 9/(s + 7)H₁ = 0.5K = 3
p =
5.Hard
R(s)+K(s + 2)(s + 3)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 3)(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 + 2)(s + 3)(s + 7))unity negative feedback
Kmax =
6.Hard
R(s)+K(s + 2)(s + 6)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 6)(s + 8)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/((s + 2)(s + 6)(s + 8))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = −16
  2. 2. T = 65
  3. 3. K = 2.25
  4. 4. p = −38.5
  5. 5. Kmax = 450
  6. 6. ω = 8.718 rad/s

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