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 + 9G(s)C(s)−

A plant G(s) = 20/(s + 9) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 20/(s + 9)unity negative feedback
p =
2.Easy
R(s)+4GC(s)0.04H+

An amplifier with gain G = 4 has positive feedback through a path with gain H = 0.04 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 4H = 0.04positive feedback
T =
3.Medium
R(s)+K(s + 2)(s + 3)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 3)) 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 + 3))unity negative feedback
K =
4.Medium
R(s)+K(s + 1)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 7)) 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 + 7))unity negative feedback
K =
5.Hard
R(s)+5s + 3G₁+4s + 2G₂C(s)4H₁−0.5H₂−

Reduce the block diagram with G₁ = 5/(s + 3), G₂ = 4/(s + 2), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 5/(s + 3)G₂ = 4/(s + 2)H₁ = 4H₂ = 0.5
T(0) =
6.Hard
R(s)+5controller+D(s)+7s + 4plantC(s)−

A proportional controller K = 5 drives the plant G(s) = 7/(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 1 is applied. Find the steady-state output css.

K = 5G(s) = 7/(s + 4)D = 1R = 0
css =

Answer key

  1. 1. p = −29
  2. 2. T = 4.762
  3. 3. K = 0.25
  4. 4. K = 9
  5. 5. T(0) = 0.3125
  6. 6. css = 0.1795

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