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)+18GC(s)0.025H+

An amplifier with gain G = 18 has positive feedback through a path with gain H = 0.025 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 18H = 0.025positive feedback
T =
2.Easy
R(s)+14GC(s)0.04H+

An amplifier with gain G = 14 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 = 14H = 0.04positive feedback
T =
3.Medium
R(s)+29s + 8G(s)C(s)0.2H−

A plant G(s) = 29/(s + 8) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. A step of size 10 is applied at R. Find the steady-state output css.

G(s) = 29/(s + 8)H = 0.2R = 10
css =
4.Medium
R(s)+11(s + 5)(s + 1)(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 11(s + 5)/((s + 1)(s + 4)). A step of size 10 is applied at the reference. Find the steady-state error ess.

G(s) = 11(s + 5)/((s + 1)(s + 4))R = 10
ess =
5.Hard
R(s)+38s(s + 12)G(s)C(s)2H−

The plant G(s) = 38/(s(s + 12)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 38/(s(s + 12))H = 2
σ =
6.Hard
R(s)+11controller+D(s)+6s + 7plantC(s)−

A proportional controller K = 11 drives the plant G(s) = 6/(s + 7) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). With R = 0, a disturbance step of size 2 is applied. Find the steady-state output css.

K = 11G(s) = 6/(s + 7)D = 2R = 0
css =

Answer key

  1. 1. T = 32.73
  2. 2. T = 31.82
  3. 3. css = 21.01
  4. 4. ess = 0.678
  5. 5. σ = −6
  6. 6. css = 0.1644

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