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)4G₂4G₃++3G₁C(s)

The signal R splits into two parallel blocks G₂ = 4 and G₃ = 4. 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 = 4G₃ = 4signs: + G₂, + G₃
T =
2.Easy
R(s)+7G₁5G₂C(s)0.5H−

In the block diagram the forward path has the gains G₁ = 7 and G₂ = 5 in series, and the negative feedback path has the gain H = 0.5. Find the overall gain T = C/R.

G₁ = 7G₂ = 5H = 0.5
T =
3.Medium
R(s)+9K+6s + 8G(s)C(s)3H₁−−

The plant G(s) = 6/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 3. A controller gain K = 9 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 6/(s + 8)H₁ = 3K = 9
T(0) =
4.Medium
R(s)+Ks(s + 15)G(s)C(s)−

The plant G(s) = K/(s(s + 15)) 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 + 15))unity negative feedback
K =
5.Hard
R(s)+15controller+D(s)+10s + 6plantC(s)−

A proportional controller K = 15 drives the plant G(s) = 10/(s + 6) 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 10 are applied together. Find the steady-state output css.

K = 15G(s) = 10/(s + 6)D = 10R = 5
css =
6.Hard
R(s)+Kcontroller+D(s)+1s + 5plantC(s)−

A proportional controller K drives the plant G(s) = 1/(s + 5) in a unity negative feedback loop. A disturbance step of size 0.5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.002.

G(s) = 1/(s + 5)D = 0.5css ≤ 0.002
K =

Answer key

  1. 1. T = 24
  2. 2. T = 1.892
  3. 3. T(0) = 0.675
  4. 4. K = 56.25
  5. 5. css = 5.449
  6. 6. K = 245

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