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)0.05H+

An amplifier with gain G = 8 has positive feedback through a path with gain H = 0.05 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 8H = 0.05positive feedback
T =
2.Easy
R(s)+5GC(s)0.04H+

An amplifier with gain G = 5 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 = 5H = 0.04positive feedback
T =
3.Medium
R(s)+46s(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 46/(s(s + 5)). The reference is a ramp r(t) = 5·t. Find the steady-state error ess.

G(s) = 46/(s(s + 5))r(t) = 5·t
ess =
4.Medium
R(s)+17s + 2G(s)C(s)0.5H−

A plant G(s) = 17/(s + 2) 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) = 17/(s + 2)H = 0.5
τ = s
5.Hard
R(s)+4s + 1G₁+3s + 8G₂C(s)4H₁−1H₂−

Reduce the block diagram with G₁ = 4/(s + 1), G₂ = 3/(s + 8), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 4/(s + 1)G₂ = 3/(s + 8)H₁ = 4H₂ = 1
T(0) =
6.Hard
R(s)+2s + 3G₁+9s + 4G₂C(s)1H₁−0.25H₂−

Reduce the block diagram with G₁ = 2/(s + 3), G₂ = 9/(s + 4), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 2/(s + 3)G₂ = 9/(s + 4)H₁ = 1H₂ = 0.25
T(0) =

Answer key

  1. 1. T = 13.33
  2. 2. T = 6.25
  3. 3. ess = 0.5435
  4. 4. τ = 0.09524 s
  5. 5. T(0) = 0.375
  6. 6. T(0) = 0.4138

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