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)+9GC(s)0.02H+

An amplifier with gain G = 9 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 9H = 0.02positive feedback
T =
2.Easy
R(s)+12GC(s)0.04H+

An amplifier with gain G = 12 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 = 12H = 0.04positive feedback
T =
3.Medium
R(s)+K(s + 8)(s + 9)G(s)C(s)−

The plant G(s) = K/((s + 8)(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 + 8)(s + 9))unity negative feedback
K =
4.Medium
R(s)+Ks(s + 19)G(s)C(s)−

The plant G(s) = K/(s(s + 19)) 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 + 19))unity negative feedback
K =
5.Hard
R(s)+18controller+D(s)+2s + 8plantC(s)−

A proportional controller K = 18 drives the plant G(s) = 2/(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 1 and a disturbance step of size 1 are applied together. Find the steady-state output css.

K = 18G(s) = 2/(s + 8)D = 1R = 1
css =
6.Hard
R(s)+26controller+D(s)+4s + 6plantC(s)−

A proportional controller K = 26 drives the plant G(s) = 4/(s + 6) 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 = 26G(s) = 4/(s + 6)D = 2R = 0
css =

Answer key

  1. 1. T = 10.98
  2. 2. T = 23.08
  3. 3. K = 0.25
  4. 4. K = 90.25
  5. 5. css = 0.8636
  6. 6. css = 0.07273

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