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)+15GC(s)0.04H+

An amplifier with gain G = 15 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 = 15H = 0.04positive feedback
T =
2.Easy
R(s)+8s + 3G(s)C(s)−

A plant G(s) = 8/(s + 3) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 8/(s + 3)unity negative feedback
T(0) =
3.Medium
R(s)+24s + 7G(s)C(s)2H−

A plant G(s) = 24/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 2. A step of size 24 is applied at R. Find the steady-state output css.

G(s) = 24/(s + 7)H = 2R = 24
css =
4.Medium
R(s)+17s + 2G(s)C(s)0.25H−

A plant G(s) = 17/(s + 2) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. Find the time constant τ of the closed loop.

G(s) = 17/(s + 2)H = 0.25
τ = s
5.Hard
R(s)+7s + 4G₁+7s + 8G₂C(s)2H₁−0.25H₂−

Reduce the block diagram with G₁ = 7/(s + 4), G₂ = 7/(s + 8), an inner negative feedback H₁ = 2 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 7/(s + 4)G₂ = 7/(s + 8)H₁ = 2H₂ = 0.25
T(0) =
6.Hard
R(s)+28controller+D(s)+8s + 1plantC(s)−

A proportional controller K = 28 drives the plant G(s) = 8/(s + 1) 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) = 8/(s + 1)D = 10R = 1
css =

Answer key

  1. 1. T = 37.5
  2. 2. T(0) = 0.7273
  3. 3. css = 10.47
  4. 4. τ = 0.16 s
  5. 5. T(0) = 0.4888
  6. 6. css = 1.351

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