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)12G₂6G₃++9G₁C(s)

The signal R splits into two parallel blocks G₂ = 12 and G₃ = 6. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 9. Find the overall gain T = C/R.

G₁ = 9G₂ = 12G₃ = 6signs: + G₂, + G₃
T =
2.Easy
R(s)10G₂8G₃++4G₁C(s)

The signal R splits into two parallel blocks G₂ = 10 and G₃ = 8. 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 = 10G₃ = 8signs: + G₂, + G₃
T =
3.Medium
R(s)+33s + 9G(s)C(s)2H−

A plant G(s) = 33/(s + 9) is controlled in a negative feedback loop whose sensor has the gain H = 2. Find the time constant τ of the closed loop.

G(s) = 33/(s + 9)H = 2
τ = s
4.Medium
R(s)+5s + 1G(s)C(s)0.2H−

A plant G(s) = 5/(s + 1) 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 + 1)H = 0.2
τ = s
5.Hard
R(s)+60s(s + 6)G(s)C(s)0.5H−

The plant G(s) = 60/(s(s + 6)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 60/(s(s + 6))H = 0.5
ωd = rad/s
6.Hard
R(s)+18s(s + 8)G(s)C(s)2H−

The plant G(s) = 18/(s(s + 8)) 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) = 18/(s(s + 8))H = 2
ωd = rad/s

Answer key

  1. 1. T = 162
  2. 2. T = 72
  3. 3. τ = 0.01333 s
  4. 4. τ = 0.5 s
  5. 5. ωd = 4.583 rad/s
  6. 6. ωd = 4.472 rad/s

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