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)3G₂1G₃++7G₁C(s)

The signal R splits into two parallel blocks G₂ = 3 and G₃ = 1. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 7. Find the overall gain T = C/R.

G₁ = 7G₂ = 3G₃ = 1signs: + G₂, + G₃
T =
2.Easy
R(s)+13s + 8G(s)C(s)−

A plant G(s) = 13/(s + 8) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 13/(s + 8)unity negative feedback
T(0) =
3.Medium
R(s)+K(s + 5)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 5)(s + 12)) 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 + 5)(s + 12))unity negative feedback
K =
4.Medium
R(s)+29s + 6G(s)C(s)0.25H−

A plant G(s) = 29/(s + 6) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. Find the time constant τ of the closed loop.

G(s) = 29/(s + 6)H = 0.25
τ = s
5.Hard
R(s)+5s + 1G₁+2s + 4G₂C(s)0.5H₁−1H₂−

Reduce the block diagram with G₁ = 5/(s + 1), G₂ = 2/(s + 4), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 5/(s + 1)G₂ = 2/(s + 4)H₁ = 0.5H₂ = 1
T(0) =
6.Hard
R(s)+Kcontroller+D(s)+10s + 9plantC(s)−

A proportional controller K drives the plant G(s) = 10/(s + 9) in a unity negative feedback loop. A disturbance step of size 10 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.5556.

G(s) = 10/(s + 9)D = 10css ≤ 0.5556
K =

Answer key

  1. 1. T = 28
  2. 2. T(0) = 0.619
  3. 3. K = 12.25
  4. 4. τ = 0.07547 s
  5. 5. T(0) = 0.6667
  6. 6. K = 17.1

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