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)+12G₁6G₂C(s)1H−

In the block diagram the forward path has the gains G₁ = 12 and G₂ = 6 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 12G₂ = 6H = 1
T =
2.Easy
R(s)5G₂9G₃++4G₁C(s)

The signal R splits into two parallel blocks G₂ = 5 and G₃ = 9. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 4. Find the overall gain T = C/R.

G₁ = 4G₂ = 5G₃ = 9signs: + G₂, + G₃
T =
3.Medium
R(s)+12s + 4G(s)C(s)2H−

A plant G(s) = 12/(s + 4) is controlled in a negative feedback loop whose sensor has the gain H = 2. A step of size 12 is applied at R. Find the steady-state output css.

G(s) = 12/(s + 4)H = 2R = 12
css =
4.Medium
R(s)+8K+1s + 5G(s)C(s)3H₁−−

The plant G(s) = 1/(s + 5) has an inner (minor) negative feedback loop with gain H₁ = 3. A controller gain K = 8 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 1/(s + 5)H₁ = 3K = 8
T(0) =
5.Hard
R(s)+26s(s + 6)G(s)C(s)2H−

The plant G(s) = 26/(s(s + 6)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 26/(s(s + 6))H = 2
ωd = rad/s
6.Hard
R(s)+40s(s + 3)G(s)C(s)1H−

The plant G(s) = 40/(s(s + 3)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 40/(s(s + 3))H = 1
σ =

Answer key

  1. 1. T = 0.9863
  2. 2. T = 56
  3. 3. css = 5.143
  4. 4. T(0) = 0.5
  5. 5. ωd = 6.557 rad/s
  6. 6. σ = −1.5

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