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)+13GC(s)0.04H+

An amplifier with gain G = 13 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 = 13H = 0.04positive feedback
T =
2.Easy
R(s)+19s + 9G(s)C(s)−

A plant G(s) = 19/(s + 9) is placed in a unity negative feedback loop. A step of size 10 is applied at R. Find the steady-state output css.

G(s) = 19/(s + 9)unity negative feedbackR = 10
css =
3.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 =
4.Medium
R(s)+24s(s + 1)G(s)C(s)−

A unity negative feedback loop has G(s) = 24/(s(s + 1)). The reference is a ramp r(t) = 10·t. Find the steady-state error ess.

G(s) = 24/(s(s + 1))r(t) = 10·t
ess =
5.Hard
R(s)+12controller+D(s)+5s + 1plantC(s)−

A proportional controller K = 12 drives the plant G(s) = 5/(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 = 12G(s) = 5/(s + 1)D = 2R = 0
css =
6.Hard
R(s)+Kcontroller+D(s)+9s + 6plantC(s)−

A proportional controller K drives the plant G(s) = 9/(s + 6) 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 0.075.

G(s) = 9/(s + 6)D = 5css ≤ 0.075
K =

Answer key

  1. 1. T = 27.08
  2. 2. css = 6.786
  3. 3. K = 25
  4. 4. ess = 0.4167
  5. 5. css = 0.1639
  6. 6. K = 66

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