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)+20G₁8G₂C(s)1H−

In the block diagram the forward path has the gains G₁ = 20 and G₂ = 8 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 20G₂ = 8H = 1
T =
2.Easy
R(s)+5GC(s)0.05H+

An amplifier with gain G = 5 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 = 5H = 0.05positive feedback
T =
3.Medium
R(s)+10K+9s + 1G(s)C(s)5H₁−−

The plant G(s) = 9/(s + 1) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 10 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 9/(s + 1)H₁ = 5K = 10
p =
4.Medium
R(s)+Ks(s + 13)G(s)C(s)−

The plant G(s) = K/(s(s + 13)) 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 + 13))unity negative feedback
K =
5.Hard
R(s)+K(s + 3)(s + 4)(s + 6)G(s)C(s)−

The plant G(s) = K/((s + 3)(s + 4)(s + 6)) 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 + 3)(s + 4)(s + 6))unity negative feedback
Kmax =
6.Hard
R(s)+15controller+D(s)+10s + 10plantC(s)−

A proportional controller K = 15 drives the plant G(s) = 10/(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 10 and a disturbance step of size 2 are applied together. Find the steady-state output css.

K = 15G(s) = 10/(s + 10)D = 2R = 10
css =

Answer key

  1. 1. T = 0.9938
  2. 2. T = 6.667
  3. 3. p = −136
  4. 4. K = 42.25
  5. 5. Kmax = 630
  6. 6. css = 9.5

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