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)+16GC(s)0.01H+

An amplifier with gain G = 16 has positive feedback through a path with gain H = 0.01 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 16H = 0.01positive feedback
T =
2.Easy
R(s)+14GC(s)0.025H+

An amplifier with gain G = 14 has positive feedback through a path with gain H = 0.025 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 14H = 0.025positive feedback
T =
3.Medium
R(s)+13K+1s + 7G(s)C(s)5H₁−−

The plant G(s) = 1/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 13 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 1/(s + 7)H₁ = 5K = 13
T(0) =
4.Medium
R(s)+17K+9s + 8G(s)C(s)3H₁−−

The plant G(s) = 9/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 3. A controller gain K = 17 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 9/(s + 8)H₁ = 3K = 17
p =
5.Hard
R(s)+Ks(s + 1)(s + 6)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(s + 6)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/(s(s + 1)(s + 6))unity negative feedback
Kmax =
6.Hard
R(s)+4s + 4G₁+2s + 7G₂C(s)4H₁−0.2H₂−

Reduce the block diagram with G₁ = 4/(s + 4), G₂ = 2/(s + 7), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.2. Find the DC gain T(0) of C(s)/R(s).

G₁ = 4/(s + 4)G₂ = 2/(s + 7)H₁ = 4H₂ = 0.2
T(0) =

Answer key

  1. 1. T = 19.05
  2. 2. T = 21.54
  3. 3. T(0) = 0.52
  4. 4. p = −188
  5. 5. Kmax = 42
  6. 6. T(0) = 0.1299

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