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)+16GC(s)0.04H+

An amplifier with gain G = 16 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 = 16H = 0.04positive feedback
T =
2.Easy
R(s)13G₂8G₃++5G₁C(s)

The signal R splits into two parallel blocks G₂ = 13 and G₃ = 8. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 5. Find the overall gain T = C/R.

G₁ = 5G₂ = 13G₃ = 8signs: + G₂, + G₃
T =
3.Medium
R(s)+28s(s + 3)G(s)C(s)−

A unity negative feedback loop has G(s) = 28/(s(s + 3)). The reference is a ramp r(t) = 1·t. Find the steady-state error ess.

G(s) = 28/(s(s + 3))r(t) = 1·t
ess =
4.Medium
R(s)+32s + 9G(s)C(s)0.25H−

A plant G(s) = 32/(s + 9) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. A step of size 5 is applied at R. Find the steady-state output css.

G(s) = 32/(s + 9)H = 0.25R = 5
css =
5.Hard
R(s)+60s(s + 4)G(s)C(s)2H−

The plant G(s) = 60/(s(s + 4)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 60/(s(s + 4))H = 2
σ =
6.Hard
R(s)+80s(s + 4)G(s)C(s)1H−

The plant G(s) = 80/(s(s + 4)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 80/(s(s + 4))H = 1
ωd = rad/s

Answer key

  1. 1. T = 44.44
  2. 2. T = 105
  3. 3. ess = 0.1071
  4. 4. css = 9.412
  5. 5. σ = −2
  6. 6. ωd = 8.718 rad/s

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