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)+18s + 7G(s)C(s)−

A plant G(s) = 18/(s + 7) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 18/(s + 7)unity negative feedback
p =
2.Easy
R(s)2G₂4G₃++2G₁C(s)

The signal R splits into two parallel blocks G₂ = 2 and G₃ = 4. 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 = 2G₃ = 4signs: + G₂, + G₃
T =
3.Medium
R(s)+K(s + 1)(s + 4)G(s)C(s)−

The plant G(s) = K/((s + 1)(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 + 1)(s + 4))unity negative feedback
K =
4.Medium
R(s)+15K+7s + 2G(s)C(s)0.5H₁−−

The plant G(s) = 7/(s + 2) has an inner (minor) negative feedback loop with gain H₁ = 0.5. A controller gain K = 15 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 7/(s + 2)H₁ = 0.5K = 15
p =
5.Hard
R(s)+K(s + 2)(s + 3)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 3)(s + 8)) 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 + 2)(s + 3)(s + 8))unity negative feedback
Kmax =
6.Hard
R(s)+Kcontroller+D(s)+2s + 7plantC(s)−

A proportional controller K drives the plant G(s) = 2/(s + 7) in a unity negative feedback loop. A disturbance step of size 1 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.002857.

G(s) = 2/(s + 7)D = 1css ≤ 0.002857
K =

Answer key

  1. 1. p = −25
  2. 2. T = 12
  3. 3. K = 2.25
  4. 4. p = −110.5
  5. 5. Kmax = 550
  6. 6. K = 346.5

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