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)+17s + 9G(s)C(s)−

A plant G(s) = 17/(s + 9) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 17/(s + 9)unity negative feedback
p =
2.Easy
R(s)+7GC(s)0.05H+

An amplifier with gain G = 7 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 = 7H = 0.05positive feedback
T =
3.Medium
R(s)+38s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 38/(s(s + 10)). The reference is a ramp r(t) = 10·t. Find the steady-state error ess.

G(s) = 38/(s(s + 10))r(t) = 10·t
ess =
4.Medium
R(s)+10(s + 2)(s + 5)(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 10(s + 2)/((s + 5)(s + 6)). A step of size 2 is applied at the reference. Find the steady-state error ess.

G(s) = 10(s + 2)/((s + 5)(s + 6))R = 2
ess =
5.Hard
R(s)+5controller+D(s)+7s + 5plantC(s)−

A proportional controller K = 5 drives the plant G(s) = 7/(s + 5) 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 0.5 are applied together. Find the steady-state output css.

K = 5G(s) = 7/(s + 5)D = 0.5R = 2
css =
6.Hard
R(s)+22controller+D(s)+8s + 7plantC(s)−

A proportional controller K = 22 drives the plant G(s) = 8/(s + 7) 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 10 is applied. Find the steady-state output css.

K = 22G(s) = 8/(s + 7)D = 10R = 0
css =

Answer key

  1. 1. p = −26
  2. 2. T = 10.77
  3. 3. ess = 2.632
  4. 4. ess = 1.2
  5. 5. css = 1.837
  6. 6. css = 0.4372

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