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)+2GC(s)0.1H+

An amplifier with gain G = 2 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 = 2H = 0.1positive feedback
T =
2.Easy
R(s)+6GC(s)0.025H+

An amplifier with gain G = 6 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 = 6H = 0.025positive feedback
T =
3.Medium
R(s)+11s + 10G(s)C(s)0.25H−

A plant G(s) = 11/(s + 10) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 11/(s + 10)H = 0.25R = 1
css =
4.Medium
R(s)+4s + 7G(s)C(s)0.5H−

A plant G(s) = 4/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 0.5. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 4/(s + 7)H = 0.5R = 1
css =
5.Hard
R(s)+11s + 3G₁+6s + 1G₂C(s)1H₁−0.5H₂−

Reduce the block diagram with G₁ = 11/(s + 3), G₂ = 6/(s + 1), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 11/(s + 3)G₂ = 6/(s + 1)H₁ = 1H₂ = 0.5
T(0) =
6.Hard
R(s)+11s + 2G₁+4s + 1G₂C(s)4H₁−0.5H₂−

Reduce the block diagram with G₁ = 11/(s + 2), G₂ = 4/(s + 1), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 11/(s + 2)G₂ = 4/(s + 1)H₁ = 4H₂ = 0.5
T(0) =

Answer key

  1. 1. T = 2.5
  2. 2. T = 7.059
  3. 3. css = 0.8627
  4. 4. css = 0.4444
  5. 5. T(0) = 1.222
  6. 6. T(0) = 0.7857

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