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)+17GC(s)0.01H+

An amplifier with gain G = 17 has positive feedback through a path with gain H = 0.01 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 17H = 0.01positive feedback
T =
2.Easy
R(s)11G₂4G₃++9G₁C(s)

The signal R splits into two parallel blocks G₂ = 11 and G₃ = 4. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 9. Find the overall gain T = C/R.

G₁ = 9G₂ = 11G₃ = 4signs: + G₂, + G₃
T =
3.Medium
R(s)+5s + 6G(s)C(s)0.25H−

A plant G(s) = 5/(s + 6) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. Find the time constant τ of the closed loop.

G(s) = 5/(s + 6)H = 0.25
τ = s
4.Medium
R(s)+19K+7s + 5G(s)C(s)0.5H₁−−

The plant G(s) = 7/(s + 5) has an inner (minor) negative feedback loop with gain H₁ = 0.5. A controller gain K = 19 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 7/(s + 5)H₁ = 0.5K = 19
p =
5.Hard
R(s)+16s + 2G₁+2s + 5G₂C(s)4H₁−0.25H₂−

Reduce the block diagram with G₁ = 16/(s + 2), G₂ = 2/(s + 5), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 16/(s + 2)G₂ = 2/(s + 5)H₁ = 4H₂ = 0.25
T(0) =
6.Hard
R(s)+Kcontroller+D(s)+2s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 2/(s + 4) in a unity negative feedback loop. A disturbance step of size 0.5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.05.

G(s) = 2/(s + 4)D = 0.5css ≤ 0.05
K =

Answer key

  1. 1. T = 20.48
  2. 2. T = 135
  3. 3. τ = 0.1379 s
  4. 4. p = −141.5
  5. 5. T(0) = 0.9412
  6. 6. K = 8

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