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)+9GC(s)0.025H+

An amplifier with gain G = 9 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 = 9H = 0.025positive feedback
T =
2.Easy
R(s)+14s + 3G(s)C(s)−

A plant G(s) = 14/(s + 3) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 14/(s + 3)unity negative feedback
τ = s
3.Medium
R(s)+K(s + 2)(s + 5)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 5)) 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 + 5))unity negative feedback
K =
4.Medium
R(s)+K(s + 1)(s + 6)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 6)) 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 + 1)(s + 6))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+2s + 9plantC(s)−

A proportional controller K drives the plant G(s) = 2/(s + 9) 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 0.04444.

G(s) = 2/(s + 9)D = 10css ≤ 0.04444
K =
6.Hard
R(s)+18controller+D(s)+8s + 5plantC(s)−

A proportional controller K = 18 drives the plant G(s) = 8/(s + 5) 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 1 is applied. Find the steady-state output css.

K = 18G(s) = 8/(s + 5)D = 1R = 0
css =

Answer key

  1. 1. T = 11.61
  2. 2. τ = 0.05882 s
  3. 3. K = 2.25
  4. 4. K = 6.25
  5. 5. K = 220.5
  6. 6. css = 0.05369

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