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)+20s + 3G(s)C(s)−

A plant G(s) = 20/(s + 3) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 20/(s + 3)unity negative feedback
p =
2.Easy
R(s)+6s + 9G(s)C(s)−

A plant G(s) = 6/(s + 9) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 6/(s + 9)unity negative feedback
T(0) =
3.Medium
R(s)+2K+10s + 1G(s)C(s)1H₁−−

The plant G(s) = 10/(s + 1) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 2 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 10/(s + 1)H₁ = 1K = 2
T(0) =
4.Medium
R(s)+18K+9s + 7G(s)C(s)2H₁−−

The plant G(s) = 9/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 18 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 9/(s + 7)H₁ = 2K = 18
T(0) =
5.Hard
R(s)+36s(s + 5)G(s)C(s)2H−

The plant G(s) = 36/(s(s + 5)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 36/(s(s + 5))H = 2
σ =
6.Hard
R(s)+Ks(s + 1)(s + 7)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(s + 7)) 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(s + 1)(s + 7))unity negative feedback
ω = rad/s

Answer key

  1. 1. p = −23
  2. 2. T(0) = 0.4
  3. 3. T(0) = 0.6452
  4. 4. T(0) = 0.8663
  5. 5. σ = −2.5
  6. 6. ω = 2.646 rad/s

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