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)2G₂12G₃+−5G₁C(s)

The signal R splits into two parallel blocks G₂ = 2 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 = 2G₃ = 12signs: + G₂, − G₃
T =
2.Easy
R(s)+9GC(s)0.05H+

An amplifier with gain G = 9 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 = 9H = 0.05positive feedback
T =
3.Medium
R(s)+6K+6s + 6G(s)C(s)0.5H₁−−

The plant G(s) = 6/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 0.5. A controller gain K = 6 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 6/(s + 6)H₁ = 0.5K = 6
p =
4.Medium
R(s)+15K+4s + 4G(s)C(s)2H₁−−

The plant G(s) = 4/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 15 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 4/(s + 4)H₁ = 2K = 15
p =
5.Hard
R(s)+9controller+D(s)+8s + 1plantC(s)−

A proportional controller K = 9 drives the plant G(s) = 8/(s + 1) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). With R = 0, a disturbance step of size 2 is applied. Find the steady-state output css.

K = 9G(s) = 8/(s + 1)D = 2R = 0
css =
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. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/(s(s + 3)(s + 5))unity negative feedback
Kmax =

Answer key

  1. 1. T = −50
  2. 2. T = 16.36
  3. 3. p = −45
  4. 4. p = −72
  5. 5. css = 0.2192
  6. 6. Kmax = 120

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