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)+17G₁1G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 17 and G₂ = 1 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 17G₂ = 1H = 0.05
T =
2.Easy
R(s)5G₂8G₃++8G₁C(s)

The signal R splits into two parallel blocks G₂ = 5 and G₃ = 8. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 8. Find the overall gain T = C/R.

G₁ = 8G₂ = 5G₃ = 8signs: + G₂, + G₃
T =
3.Medium
R(s)+K(s + 6)(s + 9)G(s)C(s)−

The plant G(s) = K/((s + 6)(s + 9)) 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 + 6)(s + 9))unity negative feedback
K =
4.Medium
R(s)+Ks(s + 19)G(s)C(s)−

The plant G(s) = K/(s(s + 19)) 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 + 19))unity negative feedback
K =
5.Hard
R(s)+13controller+D(s)+1s + 7plantC(s)−

A proportional controller K = 13 drives the plant G(s) = 1/(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 5 and a disturbance step of size 0.5 are applied together. Find the steady-state output css.

K = 13G(s) = 1/(s + 7)D = 0.5R = 5
css =
6.Hard
R(s)+K(s + 2)(s + 7)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 7)(s + 8)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/((s + 2)(s + 7)(s + 8))unity negative feedback
Kmax =

Answer key

  1. 1. T = 9.189
  2. 2. T = 104
  3. 3. K = 2.25
  4. 4. K = 90.25
  5. 5. css = 3.275
  6. 6. Kmax = 1350

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