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)0.04H+

An amplifier with gain G = 7 has positive feedback through a path with gain H = 0.04 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 7H = 0.04positive feedback
T =
2.Easy
R(s)+12GC(s)0.05H+

An amplifier with gain G = 12 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 = 12H = 0.05positive feedback
T =
3.Medium
R(s)+Ks(s + 9)G(s)C(s)−

The plant G(s) = K/(s(s + 9)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).

G(s) = K/(s(s + 9))unity negative feedback
K =
4.Medium
R(s)+Ks(s + 10)G(s)C(s)−

The plant G(s) = K/(s(s + 10)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).

G(s) = K/(s(s + 10))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+1s + 5plantC(s)−

A proportional controller K drives the plant G(s) = 1/(s + 5) 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 0.002.

G(s) = 1/(s + 5)D = 0.5css ≤ 0.002
K =
6.Hard
R(s)+Kcontroller+D(s)+2s + 8plantC(s)−

A proportional controller K drives the plant G(s) = 2/(s + 8) in a unity negative feedback loop. A disturbance step of size 2 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.005.

G(s) = 2/(s + 8)D = 2css ≤ 0.005
K =

Answer key

  1. 1. T = 9.722
  2. 2. T = 30
  3. 3. K = 20.25
  4. 4. K = 25
  5. 5. K = 245
  6. 6. K = 396

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