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)6G₂9G₃++6G₁C(s)

The signal R splits into two parallel blocks G₂ = 6 and G₃ = 9. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 6. Find the overall gain T = C/R.

G₁ = 6G₂ = 6G₃ = 9signs: + G₂, + G₃
T =
2.Easy
R(s)11G₂6G₃+−4G₁C(s)

The signal R splits into two parallel blocks G₂ = 11 and G₃ = 6. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 4. Find the overall gain T = C/R.

G₁ = 4G₂ = 11G₃ = 6signs: + G₂, − G₃
T =
3.Medium
R(s)+8(s + 7)(s + 4)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 8(s + 7)/((s + 4)(s + 9)). A step of size 1 is applied at the reference. Find the steady-state error ess.

G(s) = 8(s + 7)/((s + 4)(s + 9))R = 1
ess =
4.Medium
R(s)+9K+6s + 4G(s)C(s)3H₁−−

The plant G(s) = 6/(s + 4) 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 pole p.

G(s) = 6/(s + 4)H₁ = 3K = 9
p =
5.Hard
R(s)+K(s + 3)(s + 4)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 3)(s + 4)(s + 8)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/((s + 3)(s + 4)(s + 8))unity negative feedback
ω = rad/s
6.Hard
R(s)+19controller+D(s)+2s + 7plantC(s)−

A proportional controller K = 19 drives the plant G(s) = 2/(s + 7) 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 1 and a disturbance step of size 2 are applied together. Find the steady-state output css.

K = 19G(s) = 2/(s + 7)D = 2R = 1
css =

Answer key

  1. 1. T = 90
  2. 2. T = 20
  3. 3. ess = 0.3913
  4. 4. p = −76
  5. 5. ω = 8.246 rad/s
  6. 6. css = 0.9333

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