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)+6GC(s)0.04H+

An amplifier with gain G = 6 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 = 6H = 0.04positive feedback
T =
2.Easy
R(s)+19s + 3G(s)C(s)−

A plant G(s) = 19/(s + 3) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 19/(s + 3)unity negative feedback
p =
3.Medium
R(s)+11K+8s + 4G(s)C(s)4H₁−−

The plant G(s) = 8/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 11 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 8/(s + 4)H₁ = 4K = 11
T(0) =
4.Medium
R(s)+5K+2s + 7G(s)C(s)5H₁−−

The plant G(s) = 2/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 5 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 2/(s + 7)H₁ = 5K = 5
T(0) =
5.Hard
R(s)+3s + 5G₁+8s + 4G₂C(s)1H₁−0.1H₂−

Reduce the block diagram with G₁ = 3/(s + 5), G₂ = 8/(s + 4), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 3/(s + 5)G₂ = 8/(s + 4)H₁ = 1H₂ = 0.1
T(0) =
6.Hard
R(s)+21controller+D(s)+10s + 4plantC(s)−

A proportional controller K = 21 drives the plant G(s) = 10/(s + 4) 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 0.5 is applied. Find the steady-state output css.

K = 21G(s) = 10/(s + 4)D = 0.5R = 0
css =

Answer key

  1. 1. T = 7.895
  2. 2. p = −22
  3. 3. T(0) = 0.7097
  4. 4. T(0) = 0.3704
  5. 5. T(0) = 0.3846
  6. 6. css = 0.02336

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