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)11G₂7G₃+−7G₁C(s)

The signal R splits into two parallel blocks G₂ = 11 and G₃ = 7. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 7. Find the overall gain T = C/R.

G₁ = 7G₂ = 11G₃ = 7signs: + G₂, − G₃
T =
2.Easy
R(s)2G₂6G₃++6G₁C(s)

The signal R splits into two parallel blocks G₂ = 2 and G₃ = 6. 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 = 2G₃ = 6signs: + G₂, + G₃
T =
3.Medium
R(s)+24s(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 24/(s(s + 4)). The reference is a ramp r(t) = 1·t. Find the steady-state error ess.

G(s) = 24/(s(s + 4))r(t) = 1·t
ess =
4.Medium
R(s)+15s + 8G(s)C(s)0.2H−

A plant G(s) = 15/(s + 8) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.

G(s) = 15/(s + 8)H = 0.2
τ = s
5.Hard
R(s)+K(s + 5)(s + 6)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 5)(s + 6)(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 + 5)(s + 6)(s + 8))unity negative feedback
Kmax =
6.Hard
R(s)+22controller+D(s)+1s + 1plantC(s)−

A proportional controller K = 22 drives the plant G(s) = 1/(s + 1) 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 = 22G(s) = 1/(s + 1)D = 5R = 2
css =

Answer key

  1. 1. T = 28
  2. 2. T = 48
  3. 3. ess = 0.1667
  4. 4. τ = 0.09091 s
  5. 5. Kmax = 2002
  6. 6. css = 2.13

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