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)7G₂1G₃++2G₁C(s)

The signal R splits into two parallel blocks G₂ = 7 and G₃ = 1. 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 = 1signs: + G₂, + G₃
T =
2.Easy
R(s)+3s + 2G(s)C(s)−

A plant G(s) = 3/(s + 2) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 3/(s + 2)unity negative feedback
τ = s
3.Medium
R(s)+K(s + 2)(s + 6)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 6)) 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 + 6))unity negative feedback
K =
4.Medium
R(s)+2K+4s + 1G(s)C(s)3H₁−−

The plant G(s) = 4/(s + 1) has an inner (minor) negative feedback loop with gain H₁ = 3. 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) = 4/(s + 1)H₁ = 3K = 2
T(0) =
5.Hard
R(s)+Kcontroller+D(s)+4s + 8plantC(s)−

A proportional controller K drives the plant G(s) = 4/(s + 8) in a unity negative feedback loop. A disturbance step of size 5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.125.

G(s) = 4/(s + 8)D = 5css ≤ 0.125
K =
6.Hard
R(s)+5controller+D(s)+9s + 4plantC(s)−

A proportional controller K = 5 drives the plant G(s) = 9/(s + 4) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). With R = 0, a disturbance step of size 0.5 is applied. Find the steady-state output css.

K = 5G(s) = 9/(s + 4)D = 0.5R = 0
css =

Answer key

  1. 1. T = 16
  2. 2. τ = 0.2 s
  3. 3. K = 4
  4. 4. T(0) = 0.381
  5. 5. K = 38
  6. 6. css = 0.09184

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