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.

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1.Easy
R(s)+8GC(s)0.025H+

An amplifier with gain G = 8 has positive feedback through a path with gain H = 0.025 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 8H = 0.025positive feedback
T =
2.Easy
R(s)15G₂2G₃+−8G₁C(s)

The signal R splits into two parallel blocks G₂ = 15 and G₃ = 2. 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 = 15G₃ = 2signs: + G₂, − G₃
T =
3.Medium
R(s)+10K+1s + 2G(s)C(s)0.5H₁−−

The plant G(s) = 1/(s + 2) has an inner (minor) negative feedback loop with gain H₁ = 0.5. A controller gain K = 10 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 1/(s + 2)H₁ = 0.5K = 10
T(0) =
4.Medium
R(s)+9K+7s + 8G(s)C(s)5H₁−−

The plant G(s) = 7/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 9 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 7/(s + 8)H₁ = 5K = 9
p =
5.Hard
R(s)+66s(s + 7)G(s)C(s)0.5H−

The plant G(s) = 66/(s(s + 7)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their real part σ.

G(s) = 66/(s(s + 7))H = 0.5
σ =
6.Hard
R(s)+Ks(s + 3)(s + 5)G(s)C(s)−

The plant G(s) = K/(s(s + 3)(s + 5)) 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(s + 3)(s + 5))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = 10
  2. 2. T = 104
  3. 3. T(0) = 0.8
  4. 4. p = −106
  5. 5. σ = −3.5
  6. 6. ω = 3.873 rad/s

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