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)+14GC(s)0.02H+

An amplifier with gain G = 14 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 = 14H = 0.02positive feedback
T =
2.Easy
R(s)+12G₁9G₂C(s)1H−

In the block diagram the forward path has the gains G₁ = 12 and G₂ = 9 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 12G₂ = 9H = 1
T =
3.Medium
R(s)+Ks(s + 4)G(s)C(s)−

The plant G(s) = K/(s(s + 4)) 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(s + 4))unity negative feedback
K =
4.Medium
R(s)+Ks(s + 20)G(s)C(s)−

The plant G(s) = K/(s(s + 20)) 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(s + 20))unity negative feedback
K =
5.Hard
R(s)+11controller+D(s)+6s + 10plantC(s)−

A proportional controller K = 11 drives the plant G(s) = 6/(s + 10) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 2 and a disturbance step of size 0.5 are applied together. Find the steady-state output css.

K = 11G(s) = 6/(s + 10)D = 0.5R = 2
css =
6.Hard
R(s)+9controller+D(s)+3s + 8plantC(s)−

A proportional controller K = 9 drives the plant G(s) = 3/(s + 8) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 5 and a disturbance step of size 10 are applied together. Find the steady-state output css.

K = 9G(s) = 3/(s + 8)D = 10R = 5
css =

Answer key

  1. 1. T = 19.44
  2. 2. T = 0.9908
  3. 3. K = 4
  4. 4. K = 100
  5. 5. css = 1.776
  6. 6. css = 4.714

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