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)2G₂9G₃++4G₁C(s)

The signal R splits into two parallel blocks G₂ = 2 and G₃ = 9. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 4. Find the overall gain T = C/R.

G₁ = 4G₂ = 2G₃ = 9signs: + G₂, + G₃
T =
2.Easy
R(s)+17G₁10G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 17 and G₂ = 10 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 17G₂ = 10H = 0.25
T =
3.Medium
R(s)+K(s + 4)(s + 9)G(s)C(s)−

The plant G(s) = K/((s + 4)(s + 9)) 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 + 4)(s + 9))unity negative feedback
K =
4.Medium
R(s)+Ks(s + 16)G(s)C(s)−

The plant G(s) = K/(s(s + 16)) 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 + 16))unity negative feedback
K =
5.Hard
R(s)+K(s + 1)(s + 6)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 6)(s + 8)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/((s + 1)(s + 6)(s + 8))unity negative feedback
ω = rad/s
6.Hard
R(s)+Ks(s + 1)(s + 2)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(s + 2)) 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 + 2))unity negative feedback
Kmax =

Answer key

  1. 1. T = 44
  2. 2. T = 3.908
  3. 3. K = 6.25
  4. 4. K = 64
  5. 5. ω = 7.874 rad/s
  6. 6. Kmax = 6

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