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)0.025H+

An amplifier with gain G = 10 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 = 10H = 0.025positive feedback
T =
2.Easy
R(s)+5GC(s)0.1H+

An amplifier with gain G = 5 has positive feedback through a path with gain H = 0.1 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 5H = 0.1positive feedback
T =
3.Medium
R(s)+Ks(s + 4)G(s)C(s)−

The plant G(s) = K/(s(s + 4)) 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 + 4))unity negative feedback
K =
4.Medium
R(s)+14K+2s + 5G(s)C(s)1H₁−−

The plant G(s) = 2/(s + 5) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 14 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 2/(s + 5)H₁ = 1K = 14
T(0) =
5.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 =
6.Hard
R(s)+2controller+D(s)+3s + 8plantC(s)−

A proportional controller K = 2 drives the plant G(s) = 3/(s + 8) 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 10 is applied. Find the steady-state output css.

K = 2G(s) = 3/(s + 8)D = 10R = 0
css =

Answer key

  1. 1. T = 13.33
  2. 2. T = 10
  3. 3. K = 4
  4. 4. T(0) = 0.8
  5. 5. K = 396
  6. 6. css = 2.143

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