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)0.01H+

An amplifier with gain G = 18 has positive feedback through a path with gain H = 0.01 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 18H = 0.01positive feedback
T =
2.Easy
R(s)+11GC(s)0.05H+

An amplifier with gain G = 11 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 = 11H = 0.05positive feedback
T =
3.Medium
R(s)+20K+9s + 4G(s)C(s)4H₁−−

The plant G(s) = 9/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 20 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 9/(s + 4)H₁ = 4K = 20
T(0) =
4.Medium
R(s)+2s + 5G(s)C(s)2H−

A plant G(s) = 2/(s + 5) 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) = 2/(s + 5)H = 2
τ = s
5.Hard
R(s)+4s(s + 2)G(s)C(s)2H−

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

G(s) = 4/(s(s + 2))H = 2
σ =
6.Hard
R(s)+30controller+D(s)+6s + 5plantC(s)−

A proportional controller K = 30 drives the plant G(s) = 6/(s + 5) 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 = 30G(s) = 6/(s + 5)D = 5R = 2
css =

Answer key

  1. 1. T = 21.95
  2. 2. T = 24.44
  3. 3. T(0) = 0.8182
  4. 4. τ = 0.1111 s
  5. 5. σ = −1
  6. 6. css = 2.108

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