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)+17GC(s)0.02H+

An amplifier with gain G = 17 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 = 17H = 0.02positive feedback
T =
2.Easy
R(s)+17GC(s)0.04H+

An amplifier with gain G = 17 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 = 17H = 0.04positive feedback
T =
3.Medium
R(s)+36s + 1G(s)C(s)0.5H−

A plant G(s) = 36/(s + 1) is controlled in a negative feedback loop whose sensor has the gain H = 0.5. Find the time constant τ of the closed loop.

G(s) = 36/(s + 1)H = 0.5
τ = s
4.Medium
R(s)+9K+3s + 2G(s)C(s)0.5H₁−−

The plant G(s) = 3/(s + 2) has an inner (minor) negative feedback loop with gain H₁ = 0.5. A controller gain K = 9 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 3/(s + 2)H₁ = 0.5K = 9
p =
5.Hard
R(s)+8s + 5G₁+6s + 5G₂C(s)0.5H₁−0.5H₂−

Reduce the block diagram with G₁ = 8/(s + 5), G₂ = 6/(s + 5), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 8/(s + 5)G₂ = 6/(s + 5)H₁ = 0.5H₂ = 0.5
T(0) =
6.Hard
R(s)+9s + 2G₁+5s + 7G₂C(s)0.5H₁−0.25H₂−

Reduce the block diagram with G₁ = 9/(s + 2), G₂ = 5/(s + 7), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 9/(s + 2)G₂ = 5/(s + 7)H₁ = 0.5H₂ = 0.25
T(0) =

Answer key

  1. 1. T = 25.76
  2. 2. T = 53.13
  3. 3. τ = 0.05263 s
  4. 4. p = −30.5
  5. 5. T(0) = 0.75
  6. 6. T(0) = 1.488

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