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)+3s + 4G(s)C(s)−

A plant G(s) = 3/(s + 4) is placed in a unity negative feedback loop. A step of size 10 is applied at R. Find the steady-state output css.

G(s) = 3/(s + 4)unity negative feedbackR = 10
css =
2.Easy
R(s)+16GC(s)0.02H+

An amplifier with gain G = 16 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 16H = 0.02positive feedback
T =
3.Medium
R(s)+Ks(s + 19)G(s)C(s)−

The plant G(s) = K/(s(s + 19)) 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 + 19))unity negative feedback
K =
4.Medium
R(s)+40s + 9G(s)C(s)0.1H−

A plant G(s) = 40/(s + 9) is controlled in a negative feedback loop whose sensor has the gain H = 0.1. A step of size 10 is applied at R. Find the steady-state output css.

G(s) = 40/(s + 9)H = 0.1R = 10
css =
5.Hard
R(s)+9s + 4G₁+8s + 7G₂C(s)1H₁−0.25H₂−

Reduce the block diagram with G₁ = 9/(s + 4), G₂ = 8/(s + 7), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 9/(s + 4)G₂ = 8/(s + 7)H₁ = 1H₂ = 0.25
T(0) =
6.Hard
R(s)+10s + 3G₁+9s + 1G₂C(s)1H₁−1H₂−

Reduce the block diagram with G₁ = 10/(s + 3), G₂ = 9/(s + 1), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 10/(s + 3)G₂ = 9/(s + 1)H₁ = 1H₂ = 1
T(0) =

Answer key

  1. 1. css = 4.286
  2. 2. T = 23.53
  3. 3. K = 90.25
  4. 4. css = 30.77
  5. 5. T(0) = 0.9231
  6. 6. T(0) = 0.75

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