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)7G₂5G₃++2G₁C(s)

The signal R splits into two parallel blocks G₂ = 7 and G₃ = 5. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 2. Find the overall gain T = C/R.

G₁ = 2G₂ = 7G₃ = 5signs: + G₂, + G₃
T =
2.Easy
R(s)9G₂2G₃++10G₁C(s)

The signal R splits into two parallel blocks G₂ = 9 and G₃ = 2. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 10. Find the overall gain T = C/R.

G₁ = 10G₂ = 9G₃ = 2signs: + G₂, + G₃
T =
3.Medium
R(s)+2K+5s + 8G(s)C(s)2H₁−−

The plant G(s) = 5/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 2 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 5/(s + 8)H₁ = 2K = 2
p =
4.Medium
R(s)+2(s + 8)(s + 7)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 2(s + 8)/((s + 7)(s + 9)). A step of size 10 is applied at the reference. Find the steady-state error ess.

G(s) = 2(s + 8)/((s + 7)(s + 9))R = 10
ess =
5.Hard
R(s)+4s + 3G₁+2s + 3G₂C(s)0.5H₁−0.2H₂−

Reduce the block diagram with G₁ = 4/(s + 3), G₂ = 2/(s + 3), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.2. Find the DC gain T(0) of C(s)/R(s).

G₁ = 4/(s + 3)G₂ = 2/(s + 3)H₁ = 0.5H₂ = 0.2
T(0) =
6.Hard
R(s)+Kcontroller+D(s)+6s + 5plantC(s)−

A proportional controller K drives the plant G(s) = 6/(s + 5) 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 0.12.

G(s) = 6/(s + 5)D = 1css ≤ 0.12
K =

Answer key

  1. 1. T = 24
  2. 2. T = 110
  3. 3. p = −28
  4. 4. ess = 7.975
  5. 5. T(0) = 0.5882
  6. 6. K = 7.5

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