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)+20GC(s)0.02H+

An amplifier with gain G = 20 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 20H = 0.02positive feedback
T =
2.Easy
R(s)+15G₁7G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 15 and G₂ = 7 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 15G₂ = 7H = 0.25
T =
3.Medium
R(s)+19K+5s + 8G(s)C(s)2H₁−−

The plant G(s) = 5/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 19 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 5/(s + 8)H₁ = 2K = 19
T(0) =
4.Medium
R(s)+19K+7s + 7G(s)C(s)1H₁−−

The plant G(s) = 7/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 19 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 7/(s + 7)H₁ = 1K = 19
p =
5.Hard
R(s)+2s + 1G₁+9s + 3G₂C(s)4H₁−1H₂−

Reduce the block diagram with G₁ = 2/(s + 1), G₂ = 9/(s + 3), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 2/(s + 1)G₂ = 9/(s + 3)H₁ = 4H₂ = 1
T(0) =
6.Hard
R(s)+6controller+D(s)+10s + 5plantC(s)−

A proportional controller K = 6 drives the plant G(s) = 10/(s + 5) 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 = 6G(s) = 10/(s + 5)D = 2R = 0
css =

Answer key

  1. 1. T = 33.33
  2. 2. T = 3.853
  3. 3. T(0) = 0.8407
  4. 4. p = −147
  5. 5. T(0) = 0.3158
  6. 6. css = 0.3077

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