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)+10GC(s)0.05H+

An amplifier with gain G = 10 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 = 10H = 0.05positive feedback
T =
2.Easy
R(s)+16GC(s)0.04H+

An amplifier with gain G = 16 has positive feedback through a path with gain H = 0.04 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 16H = 0.04positive feedback
T =
3.Medium
R(s)+21s + 6G(s)C(s)0.25H−

A plant G(s) = 21/(s + 6) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. A step of size 12 is applied at R. Find the steady-state output css.

G(s) = 21/(s + 6)H = 0.25R = 12
css =
4.Medium
R(s)+3s + 9G(s)C(s)0.2H−

A plant G(s) = 3/(s + 9) 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) = 3/(s + 9)H = 0.2
τ = s
5.Hard
R(s)+Kcontroller+D(s)+6s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 6/(s + 4) in a unity negative feedback loop. A disturbance step of size 1 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.03.

G(s) = 6/(s + 4)D = 1css ≤ 0.03
K =
6.Hard
R(s)+38s(s + 4)G(s)C(s)2H−

The plant G(s) = 38/(s(s + 4)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 38/(s(s + 4))H = 2
ωd = rad/s

Answer key

  1. 1. T = 20
  2. 2. T = 44.44
  3. 3. css = 22.4
  4. 4. τ = 0.1042 s
  5. 5. K = 32.67
  6. 6. ωd = 8.485 rad/s

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