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)+12GC(s)0.04H+

An amplifier with gain G = 12 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 = 12H = 0.04positive feedback
T =
2.Easy
R(s)11G₂9G₃++4G₁C(s)

The signal R splits into two parallel blocks G₂ = 11 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 = 11G₃ = 9signs: + G₂, + G₃
T =
3.Medium
R(s)+14s + 2G(s)C(s)0.5H−

A plant G(s) = 14/(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) = 14/(s + 2)H = 0.5
τ = s
4.Medium
R(s)+Ks(s + 16)G(s)C(s)−

The plant G(s) = K/(s(s + 16)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).

G(s) = K/(s(s + 16))unity negative feedback
K =
5.Hard
R(s)+29controller+D(s)+2s + 2plantC(s)−

A proportional controller K = 29 drives the plant G(s) = 2/(s + 2) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 5 and a disturbance step of size 1 are applied together. Find the steady-state output css.

K = 29G(s) = 2/(s + 2)D = 1R = 5
css =
6.Hard
R(s)+26s(s + 8)G(s)C(s)1H−

The plant G(s) = 26/(s(s + 8)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 26/(s(s + 8))H = 1
σ =

Answer key

  1. 1. T = 23.08
  2. 2. T = 80
  3. 3. τ = 0.1111 s
  4. 4. K = 64
  5. 5. css = 4.867
  6. 6. σ = −4

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