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)+11G₁8G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 11 and G₂ = 8 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 11G₂ = 8H = 0.1
T =
2.Easy
R(s)+10s + 3G(s)C(s)−

A plant G(s) = 10/(s + 3) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 10/(s + 3)unity negative feedback
τ = s
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)+6(s + 5)(s + 2)(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 6(s + 5)/((s + 2)(s + 4)). A step of size 2 is applied at the reference. Find the steady-state error ess.

G(s) = 6(s + 5)/((s + 2)(s + 4))R = 2
ess =
5.Hard
R(s)+7controller+D(s)+6s + 3plantC(s)−

A proportional controller K = 7 drives the plant G(s) = 6/(s + 3) 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 1 and a disturbance step of size 1 are applied together. Find the steady-state output css.

K = 7G(s) = 6/(s + 3)D = 1R = 1
css =
6.Hard
R(s)+Kcontroller+D(s)+7s + 5plantC(s)−

A proportional controller K drives the plant G(s) = 7/(s + 5) in a unity negative feedback loop. A disturbance step of size 5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.14.

G(s) = 7/(s + 5)D = 5css ≤ 0.14
K =

Answer key

  1. 1. T = 8.98
  2. 2. τ = 0.07692 s
  3. 3. K = 4
  4. 4. ess = 0.4211
  5. 5. css = 1.067
  6. 6. K = 35

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