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)+18GC(s)0.02H+

An amplifier with gain G = 18 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 18H = 0.02positive feedback
T =
2.Easy
R(s)+14s + 10G(s)C(s)−

A plant G(s) = 14/(s + 10) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 14/(s + 10)unity negative feedback
p =
3.Medium
R(s)+18K+10s + 6G(s)C(s)4H₁−−

The plant G(s) = 10/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 18 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 10/(s + 6)H₁ = 4K = 18
T(0) =
4.Medium
R(s)+K(s + 6)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 6)(s + 8)) 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 + 6)(s + 8))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+9s + 8plantC(s)−

A proportional controller K drives the plant G(s) = 9/(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 0.05625.

G(s) = 9/(s + 8)D = 0.5css ≤ 0.05625
K =
6.Hard
R(s)+9s + 4G₁+1s + 8G₂C(s)0.5H₁−0.5H₂−

Reduce the block diagram with G₁ = 9/(s + 4), G₂ = 1/(s + 8), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 9/(s + 4)G₂ = 1/(s + 8)H₁ = 0.5H₂ = 0.5
T(0) =

Answer key

  1. 1. T = 28.13
  2. 2. p = −24
  3. 3. T(0) = 0.7965
  4. 4. K = 1
  5. 5. K = 8
  6. 6. T(0) = 0.2338

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