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)+8GC(s)0.025H+

An amplifier with gain G = 8 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 = 8H = 0.025positive feedback
T =
2.Easy
R(s)+8G₁3G₂C(s)0.5H−

In the block diagram the forward path has the gains G₁ = 8 and G₂ = 3 in series, and the negative feedback path has the gain H = 0.5. Find the overall gain T = C/R.

G₁ = 8G₂ = 3H = 0.5
T =
3.Medium
R(s)+3K+2s + 4G(s)C(s)2H₁−−

The plant G(s) = 2/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 3 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 2/(s + 4)H₁ = 2K = 3
T(0) =
4.Medium
R(s)+24s + 2G(s)C(s)0.2H−

A plant G(s) = 24/(s + 2) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.

G(s) = 24/(s + 2)H = 0.2
τ = s
5.Hard
R(s)+2controller+D(s)+10s + 5plantC(s)−

A proportional controller K = 2 drives the plant G(s) = 10/(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 2 and a disturbance step of size 1 are applied together. Find the steady-state output css.

K = 2G(s) = 10/(s + 5)D = 1R = 2
css =
6.Hard
R(s)+Kcontroller+D(s)+4s + 2plantC(s)−

A proportional controller K drives the plant G(s) = 4/(s + 2) 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 0.08.

G(s) = 4/(s + 2)D = 2css ≤ 0.08
K =

Answer key

  1. 1. T = 10
  2. 2. T = 1.846
  3. 3. T(0) = 0.4286
  4. 4. τ = 0.1471 s
  5. 5. css = 2
  6. 6. K = 24.5

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