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)+5GC(s)0.05H+

An amplifier with gain G = 5 has positive feedback through a path with gain H = 0.05 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 5H = 0.05positive feedback
T =
2.Easy
R(s)+6s + 7G(s)C(s)−

A plant G(s) = 6/(s + 7) is placed in a unity negative feedback loop. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 6/(s + 7)unity negative feedbackR = 1
css =
3.Medium
R(s)+30s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 30/(s(s + 10)). The reference is a ramp r(t) = 1·t. Find the steady-state error ess.

G(s) = 30/(s(s + 10))r(t) = 1·t
ess =
4.Medium
R(s)+3K+5s + 8G(s)C(s)5H₁−−

The plant G(s) = 5/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 3 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 5/(s + 8)H₁ = 5K = 3
T(0) =
5.Hard
R(s)+13s + 3G₁+3s + 3G₂C(s)0.5H₁−0.1H₂−

Reduce the block diagram with G₁ = 13/(s + 3), G₂ = 3/(s + 3), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 13/(s + 3)G₂ = 3/(s + 3)H₁ = 0.5H₂ = 0.1
T(0) =
6.Hard
R(s)+Kcontroller+D(s)+6s + 8plantC(s)−

A proportional controller K drives the plant G(s) = 6/(s + 8) in a unity negative feedback loop. A disturbance step of size 2 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.15.

G(s) = 6/(s + 8)D = 2css ≤ 0.15
K =

Answer key

  1. 1. T = 6.667
  2. 2. css = 0.4615
  3. 3. ess = 0.3333
  4. 4. T(0) = 0.3125
  5. 5. T(0) = 2.241
  6. 6. K = 12

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