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)+16s + 10G(s)C(s)−

A plant G(s) = 16/(s + 10) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 16/(s + 10)unity negative feedback
τ = s
2.Easy
R(s)+20GC(s)0.04H+

An amplifier with gain G = 20 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 = 20H = 0.04positive feedback
T =
3.Medium
R(s)+5s + 4G(s)C(s)0.2H−

A plant G(s) = 5/(s + 4) 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) = 5/(s + 4)H = 0.2
τ = s
4.Medium
R(s)+10K+7s + 7G(s)C(s)1H₁−−

The plant G(s) = 7/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 10 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 7/(s + 7)H₁ = 1K = 10
T(0) =
5.Hard
R(s)+10s + 5G₁+5s + 6G₂C(s)2H₁−0.25H₂−

Reduce the block diagram with G₁ = 10/(s + 5), G₂ = 5/(s + 6), 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 = 10/(s + 5)G₂ = 5/(s + 6)H₁ = 2H₂ = 0.25
T(0) =
6.Hard
R(s)+18s(s + 9)G(s)C(s)2H−

The plant G(s) = 18/(s(s + 9)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 18/(s(s + 9))H = 2
σ =

Answer key

  1. 1. τ = 0.03846 s
  2. 2. T = 100
  3. 3. τ = 0.2 s
  4. 4. T(0) = 0.8333
  5. 5. T(0) = 0.5405
  6. 6. σ = −4.5

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