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)0.05H+

An amplifier with gain G = 12 has positive feedback through a path with gain H = 0.05 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 12H = 0.05positive feedback
T =
2.Easy
R(s)7G₂6G₃++3G₁C(s)

The signal R splits into two parallel blocks G₂ = 7 and G₃ = 6. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 3. Find the overall gain T = C/R.

G₁ = 3G₂ = 7G₃ = 6signs: + G₂, + G₃
T =
3.Medium
R(s)+18s(s + 3)G(s)C(s)−

A unity negative feedback loop has G(s) = 18/(s(s + 3)). The reference is a ramp r(t) = 2·t. Find the steady-state error ess.

G(s) = 18/(s(s + 3))r(t) = 2·t
ess =
4.Medium
R(s)+12(s + 5)(s + 1)(s + 3)G(s)C(s)−

A unity negative feedback loop has G(s) = 12(s + 5)/((s + 1)(s + 3)). A step of size 1 is applied at the reference. Find the steady-state error ess.

G(s) = 12(s + 5)/((s + 1)(s + 3))R = 1
ess =
5.Hard
R(s)+19controller+D(s)+4s + 10plantC(s)−

A proportional controller K = 19 drives the plant G(s) = 4/(s + 10) 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 2 and a disturbance step of size 5 are applied together. Find the steady-state output css.

K = 19G(s) = 4/(s + 10)D = 5R = 2
css =
6.Hard
R(s)+30s(s + 3)G(s)C(s)1H−

The plant G(s) = 30/(s(s + 3)) 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) = 30/(s(s + 3))H = 1
ωd = rad/s

Answer key

  1. 1. T = 30
  2. 2. T = 39
  3. 3. ess = 0.3333
  4. 4. ess = 0.04762
  5. 5. css = 2
  6. 6. ωd = 5.268 rad/s

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