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)+11G₁10G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 11 and G₂ = 10 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 11G₂ = 10H = 0.05
T =
2.Easy
R(s)+2G₁10G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 2 and G₂ = 10 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 2G₂ = 10H = 0.1
T =
3.Medium
R(s)+6(s + 5)(s + 4)(s + 7)G(s)C(s)−

A unity negative feedback loop has G(s) = 6(s + 5)/((s + 4)(s + 7)). A step of size 1 is applied at the reference. Find the steady-state error ess.

G(s) = 6(s + 5)/((s + 4)(s + 7))R = 1
ess =
4.Medium
R(s)+11(s + 2)(s + 4)(s + 7)G(s)C(s)−

A unity negative feedback loop has G(s) = 11(s + 2)/((s + 4)(s + 7)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 11(s + 2)/((s + 4)(s + 7))R = 5
ess =
5.Hard
R(s)+Kcontroller+D(s)+8s + 3plantC(s)−

A proportional controller K drives the plant G(s) = 8/(s + 3) 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 0.5333.

G(s) = 8/(s + 3)D = 10css ≤ 0.5333
K =
6.Hard
R(s)+Kcontroller+D(s)+8s + 8plantC(s)−

A proportional controller K drives the plant G(s) = 8/(s + 8) in a unity negative feedback loop. A disturbance step of size 0.5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.01.

G(s) = 8/(s + 8)D = 0.5css ≤ 0.01
K =

Answer key

  1. 1. T = 16.92
  2. 2. T = 6.667
  3. 3. ess = 0.4828
  4. 4. ess = 2.8
  5. 5. K = 18.38
  6. 6. K = 49

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