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)+1s + 10G(s)C(s)−

A plant G(s) = 1/(s + 10) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 1/(s + 10)unity negative feedback
p =
2.Easy
R(s)3G₂6G₃+−5G₁C(s)

The signal R splits into two parallel blocks G₂ = 3 and G₃ = 6. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 5. Find the overall gain T = C/R.

G₁ = 5G₂ = 3G₃ = 6signs: + G₂, − G₃
T =
3.Medium
R(s)+Ks(s + 4)G(s)C(s)−

The plant G(s) = K/(s(s + 4)) 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 + 4))unity negative feedback
K =
4.Medium
R(s)+K(s + 2)(s + 10)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 10)) 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 + 2)(s + 10))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+7s + 3plantC(s)−

A proportional controller K drives the plant G(s) = 7/(s + 3) in a unity negative feedback loop. A disturbance step of size 0.5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.1167.

G(s) = 7/(s + 3)D = 0.5css ≤ 0.1167
K =
6.Hard
R(s)+Ks(s + 7)(s + 8)G(s)C(s)−

The plant G(s) = K/(s(s + 7)(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(s + 7)(s + 8))unity negative feedback
ω = rad/s

Answer key

  1. 1. p = −11
  2. 2. T = −15
  3. 3. K = 4
  4. 4. K = 16
  5. 5. K = 3.857
  6. 6. ω = 7.483 rad/s

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