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)+20G₁10G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 20 and G₂ = 10 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 20G₂ = 10H = 0.05
T =
2.Easy
R(s)+3GC(s)0.05H+

An amplifier with gain G = 3 has positive feedback through a path with gain H = 0.05 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 3H = 0.05positive feedback
T =
3.Medium
R(s)+1(s + 2)(s + 8)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 1(s + 2)/((s + 8)(s + 9)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 1(s + 2)/((s + 8)(s + 9))R = 5
ess =
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)+5s + 9plantC(s)−

A proportional controller K = 13 drives the plant G(s) = 5/(s + 9) 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 = 13G(s) = 5/(s + 9)D = 2R = 0
css =
6.Hard
R(s)+16controller+D(s)+3s + 10plantC(s)−

A proportional controller K = 16 drives the plant G(s) = 3/(s + 10) 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 = 16G(s) = 3/(s + 10)D = 10R = 5
css =

Answer key

  1. 1. T = 18.18
  2. 2. T = 3.529
  3. 3. ess = 4.865
  4. 4. K = 90.25
  5. 5. css = 0.1351
  6. 6. css = 4.655

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