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)+13s + 7G(s)C(s)−

A plant G(s) = 13/(s + 7) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 13/(s + 7)unity negative feedback
p =
2.Easy
R(s)+12GC(s)0.05H+

An amplifier with gain G = 12 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 = 12H = 0.05positive feedback
T =
3.Medium
R(s)+14s + 9G(s)C(s)2H−

A plant G(s) = 14/(s + 9) is controlled in a negative feedback loop whose sensor has the gain H = 2. A step of size 12 is applied at R. Find the steady-state output css.

G(s) = 14/(s + 9)H = 2R = 12
css =
4.Medium
R(s)+12(s + 6)(s + 1)(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 12(s + 6)/((s + 1)(s + 4)). A step of size 1 is applied at the reference. Find the steady-state error ess.

G(s) = 12(s + 6)/((s + 1)(s + 4))R = 1
ess =
5.Hard
R(s)+Kcontroller+D(s)+7s + 6plantC(s)−

A proportional controller K drives the plant G(s) = 7/(s + 6) in a unity negative feedback loop. A disturbance step of size 10 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.2333.

G(s) = 7/(s + 6)D = 10css ≤ 0.2333
K =
6.Hard
R(s)+42s(s + 7)G(s)C(s)1H−

The plant G(s) = 42/(s(s + 7)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 42/(s(s + 7))H = 1
σ =

Answer key

  1. 1. p = −20
  2. 2. T = 30
  3. 3. css = 4.541
  4. 4. ess = 0.05263
  5. 5. K = 42
  6. 6. σ = −3.5

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