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)+3s + 10G(s)C(s)−

A plant G(s) = 3/(s + 10) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 3/(s + 10)unity negative feedback
p =
2.Easy
R(s)+9GC(s)0.025H+

An amplifier with gain G = 9 has positive feedback through a path with gain H = 0.025 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 9H = 0.025positive feedback
T =
3.Medium
R(s)+Ks(s + 15)G(s)C(s)−

The plant G(s) = K/(s(s + 15)) 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 + 15))unity negative feedback
K =
4.Medium
R(s)+Ks(s + 14)G(s)C(s)−

The plant G(s) = K/(s(s + 14)) 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 + 14))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+1s + 8plantC(s)−

A proportional controller K drives the plant G(s) = 1/(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 0.05.

G(s) = 1/(s + 8)D = 2css ≤ 0.05
K =
6.Hard
R(s)+24controller+D(s)+7s + 6plantC(s)−

A proportional controller K = 24 drives the plant G(s) = 7/(s + 6) 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 5 and a disturbance step of size 0.5 are applied together. Find the steady-state output css.

K = 24G(s) = 7/(s + 6)D = 0.5R = 5
css =

Answer key

  1. 1. p = −13
  2. 2. T = 11.61
  3. 3. K = 56.25
  4. 4. K = 49
  5. 5. K = 32
  6. 6. css = 4.848

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