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)5G₂9G₃+−6G₁C(s)

The signal R splits into two parallel blocks G₂ = 5 and G₃ = 9. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 6. Find the overall gain T = C/R.

G₁ = 6G₂ = 5G₃ = 9signs: + G₂, − G₃
T =
2.Easy
R(s)+12G₁1G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 12 and G₂ = 1 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 12G₂ = 1H = 0.1
T =
3.Medium
R(s)+K(s + 1)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 12)) 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 + 1)(s + 12))unity negative feedback
K =
4.Medium
R(s)+Ks(s + 19)G(s)C(s)−

The plant G(s) = K/(s(s + 19)) 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(s + 19))unity negative feedback
K =
5.Hard
R(s)+20s + 2G₁+2s + 1G₂C(s)1H₁−0.25H₂−

Reduce the block diagram with G₁ = 20/(s + 2), G₂ = 2/(s + 1), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 20/(s + 2)G₂ = 2/(s + 1)H₁ = 1H₂ = 0.25
T(0) =
6.Hard
R(s)+K(s + 5)(s + 6)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 5)(s + 6)(s + 8)) 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 + 5)(s + 6)(s + 8))unity negative feedback
Kmax =

Answer key

  1. 1. T = −24
  2. 2. T = 5.455
  3. 3. K = 30.25
  4. 4. K = 90.25
  5. 5. T(0) = 2.5
  6. 6. Kmax = 2002

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