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)7G₂8G₃+−2G₁C(s)

The signal R splits into two parallel blocks G₂ = 7 and G₃ = 8. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 2. Find the overall gain T = C/R.

G₁ = 2G₂ = 7G₃ = 8signs: + G₂, − G₃
T =
2.Easy
R(s)+17G₁5G₂C(s)0.5H−

In the block diagram the forward path has the gains G₁ = 17 and G₂ = 5 in series, and the negative feedback path has the gain H = 0.5. Find the overall gain T = C/R.

G₁ = 17G₂ = 5H = 0.5
T =
3.Medium
R(s)+6K+7s + 7G(s)C(s)3H₁−−

The plant G(s) = 7/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 3. A controller gain K = 6 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 7/(s + 7)H₁ = 3K = 6
T(0) =
4.Medium
R(s)+K(s + 1)(s + 5)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 5)) 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 + 5))unity negative feedback
K =
5.Hard
R(s)+Ks(s + 2)(s + 5)G(s)C(s)−

The plant G(s) = K/(s(s + 2)(s + 5)) 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 + 2)(s + 5))unity negative feedback
Kmax =
6.Hard
R(s)+K(s + 1)(s + 4)(s + 5)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 4)(s + 5)) 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 + 4)(s + 5))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = −2
  2. 2. T = 1.954
  3. 3. T(0) = 0.6
  4. 4. K = 4
  5. 5. Kmax = 70
  6. 6. ω = 5.385 rad/s

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