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)0.05H+

An amplifier with gain G = 11 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 = 11H = 0.05positive feedback
T =
2.Easy
R(s)+13GC(s)0.025H+

An amplifier with gain G = 13 has positive feedback through a path with gain H = 0.025 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 13H = 0.025positive feedback
T =
3.Medium
R(s)+K(s + 2)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 12)) 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 + 2)(s + 12))unity negative feedback
K =
4.Medium
R(s)+40s + 10G(s)C(s)0.1H−

A plant G(s) = 40/(s + 10) is controlled in a negative feedback loop whose sensor has the gain H = 0.1. Find the time constant τ of the closed loop.

G(s) = 40/(s + 10)H = 0.1
τ = s
5.Hard
R(s)+Ks(s + 3)(s + 7)G(s)C(s)−

The plant G(s) = K/(s(s + 3)(s + 7)) 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(s + 3)(s + 7))unity negative feedback
Kmax =
6.Hard
R(s)+19controller+D(s)+5s + 6plantC(s)−

A proportional controller K = 19 drives the plant G(s) = 5/(s + 6) 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 2 is applied. Find the steady-state output css.

K = 19G(s) = 5/(s + 6)D = 2R = 0
css =

Answer key

  1. 1. T = 24.44
  2. 2. T = 19.26
  3. 3. K = 25
  4. 4. τ = 0.07143 s
  5. 5. Kmax = 210
  6. 6. css = 0.09901

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