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)+6G₁3G₂C(s)0.2H−

In the block diagram the forward path has the gains G₁ = 6 and G₂ = 3 in series, and the negative feedback path has the gain H = 0.2. Find the overall gain T = C/R.

G₁ = 6G₂ = 3H = 0.2
T =
2.Easy
R(s)+19GC(s)0.04H+

An amplifier with gain G = 19 has positive feedback through a path with gain H = 0.04 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 19H = 0.04positive feedback
T =
3.Medium
R(s)+8(s + 5)(s + 1)(s + 3)G(s)C(s)−

A unity negative feedback loop has G(s) = 8(s + 5)/((s + 1)(s + 3)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 8(s + 5)/((s + 1)(s + 3))R = 5
ess =
4.Medium
R(s)+11K+8s + 6G(s)C(s)2H₁−−

The plant G(s) = 8/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 11 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 8/(s + 6)H₁ = 2K = 11
p =
5.Hard
R(s)+Kcontroller+D(s)+1s + 10plantC(s)−

A proportional controller K drives the plant G(s) = 1/(s + 10) 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 0.0025.

G(s) = 1/(s + 10)D = 0.5css ≤ 0.0025
K =
6.Hard
R(s)+30controller+D(s)+6s + 5plantC(s)−

A proportional controller K = 30 drives the plant G(s) = 6/(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 = 30G(s) = 6/(s + 5)D = 1R = 0
css =

Answer key

  1. 1. T = 3.913
  2. 2. T = 79.17
  3. 3. ess = 0.3488
  4. 4. p = −110
  5. 5. K = 190
  6. 6. css = 0.03243

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