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)+16G₁9G₂C(s)1H−

In the block diagram the forward path has the gains G₁ = 16 and G₂ = 9 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 16G₂ = 9H = 1
T =
2.Easy
R(s)9G₂6G₃++10G₁C(s)

The signal R splits into two parallel blocks G₂ = 9 and G₃ = 6. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 10. Find the overall gain T = C/R.

G₁ = 10G₂ = 9G₃ = 6signs: + G₂, + G₃
T =
3.Medium
R(s)+Ks(s + 13)G(s)C(s)−

The plant G(s) = K/(s(s + 13)) 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 + 13))unity negative feedback
K =
4.Medium
R(s)+5K+2s + 2G(s)C(s)5H₁−−

The plant G(s) = 2/(s + 2) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 5 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 2/(s + 2)H₁ = 5K = 5
p =
5.Hard
R(s)+K(s + 1)(s + 5)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 5)(s + 7)) 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 + 1)(s + 5)(s + 7))unity negative feedback
Kmax =
6.Hard
R(s)+62s(s + 7)G(s)C(s)0.5H−

The plant G(s) = 62/(s(s + 7)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their real part σ.

G(s) = 62/(s(s + 7))H = 0.5
σ =

Answer key

  1. 1. T = 0.9931
  2. 2. T = 150
  3. 3. K = 42.25
  4. 4. p = −22
  5. 5. Kmax = 576
  6. 6. σ = −3.5

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