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)+10GC(s)0.02H+

An amplifier with gain G = 10 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 = 10H = 0.02positive feedback
T =
2.Easy
R(s)+12s + 7G(s)C(s)−

A plant G(s) = 12/(s + 7) 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) = 12/(s + 7)unity negative feedbackR = 10
css =
3.Medium
R(s)+K(s + 5)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 5)(s + 8)) 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 + 5)(s + 8))unity negative feedback
K =
4.Medium
R(s)+11K+8s + 6G(s)C(s)2H₁−−

The plant G(s) = 8/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 11 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 8/(s + 6)H₁ = 2K = 11
p =
5.Hard
R(s)+Kcontroller+D(s)+8s + 5plantC(s)−

A proportional controller K drives the plant G(s) = 8/(s + 5) in a unity negative feedback loop. A disturbance step of size 10 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.16.

G(s) = 8/(s + 5)D = 10css ≤ 0.16
K =
6.Hard
R(s)+28controller+D(s)+3s + 5plantC(s)−

A proportional controller K = 28 drives the plant G(s) = 3/(s + 5) 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 10 are applied together. Find the steady-state output css.

K = 28G(s) = 3/(s + 5)D = 10R = 1
css =

Answer key

  1. 1. T = 12.5
  2. 2. css = 6.316
  3. 3. K = 2.25
  4. 4. p = −110
  5. 5. K = 61.88
  6. 6. css = 1.281

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