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)+7GC(s)0.05H+

An amplifier with gain G = 7 has positive feedback through a path with gain H = 0.05 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 7H = 0.05positive feedback
T =
2.Easy
R(s)6G₂12G₃++5G₁C(s)

The signal R splits into two parallel blocks G₂ = 6 and G₃ = 12. 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 = 6G₃ = 12signs: + G₂, + G₃
T =
3.Medium
R(s)+8K+5s + 5G(s)C(s)2H₁−−

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

G(s) = 5/(s + 5)H₁ = 2K = 8
p =
4.Medium
R(s)+33s + 5G(s)C(s)0.2H−

A plant G(s) = 33/(s + 5) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.

G(s) = 33/(s + 5)H = 0.2
τ = s
5.Hard
R(s)+11controller+D(s)+1s + 8plantC(s)−

A proportional controller K = 11 drives the plant G(s) = 1/(s + 8) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 2 and a disturbance step of size 2 are applied together. Find the steady-state output css.

K = 11G(s) = 1/(s + 8)D = 2R = 2
css =
6.Hard
R(s)+Kcontroller+D(s)+2s + 9plantC(s)−

A proportional controller K drives the plant G(s) = 2/(s + 9) in a unity negative feedback loop. A disturbance step of size 5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.05556.

G(s) = 2/(s + 9)D = 5css ≤ 0.05556
K =

Answer key

  1. 1. T = 10.77
  2. 2. T = 90
  3. 3. p = −55
  4. 4. τ = 0.08621 s
  5. 5. css = 1.263
  6. 6. K = 85.5

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