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)+11GC(s)0.02H+

An amplifier with gain G = 11 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 11H = 0.02positive feedback
T =
2.Easy
R(s)+15GC(s)0.02H+

An amplifier with gain G = 15 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 15H = 0.02positive feedback
T =
3.Medium
R(s)+39s + 1G(s)C(s)0.25H−

A plant G(s) = 39/(s + 1) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. Find the time constant τ of the closed loop.

G(s) = 39/(s + 1)H = 0.25
τ = s
4.Medium
R(s)+K(s + 6)(s + 9)G(s)C(s)−

The plant G(s) = K/((s + 6)(s + 9)) 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 + 6)(s + 9))unity negative feedback
K =
5.Hard
R(s)+72s(s + 11)G(s)C(s)1H−

The plant G(s) = 72/(s(s + 11)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 72/(s(s + 11))H = 1
ωd = rad/s
6.Hard
R(s)+Kcontroller+D(s)+5s + 2plantC(s)−

A proportional controller K drives the plant G(s) = 5/(s + 2) 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 0.25.

G(s) = 5/(s + 2)D = 10css ≤ 0.25
K =

Answer key

  1. 1. T = 14.1
  2. 2. T = 21.43
  3. 3. τ = 0.09302 s
  4. 4. K = 2.25
  5. 5. ωd = 6.461 rad/s
  6. 6. K = 39.6

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