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)+14G₁2G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 14 and G₂ = 2 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 14G₂ = 2H = 0.1
T =
2.Easy
R(s)10G₂12G₃++5G₁C(s)

The signal R splits into two parallel blocks G₂ = 10 and G₃ = 12. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 5. Find the overall gain T = C/R.

G₁ = 5G₂ = 10G₃ = 12signs: + G₂, + G₃
T =
3.Medium
R(s)+25s + 6G(s)C(s)0.1H−

A plant G(s) = 25/(s + 6) is controlled in a negative feedback loop whose sensor has the gain H = 0.1. A step of size 24 is applied at R. Find the steady-state output css.

G(s) = 25/(s + 6)H = 0.1R = 24
css =
4.Medium
R(s)+K(s + 6)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 6)(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 + 6)(s + 12))unity negative feedback
K =
5.Hard
R(s)+6s + 4G₁+3s + 6G₂C(s)4H₁−0.25H₂−

Reduce the block diagram with G₁ = 6/(s + 4), G₂ = 3/(s + 6), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 6/(s + 4)G₂ = 3/(s + 6)H₁ = 4H₂ = 0.25
T(0) =
6.Hard
R(s)+6controller+D(s)+4s + 8plantC(s)−

A proportional controller K = 6 drives the plant G(s) = 4/(s + 8) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 5 and a disturbance step of size 2 are applied together. Find the steady-state output css.

K = 6G(s) = 4/(s + 8)D = 2R = 5
css =

Answer key

  1. 1. T = 7.368
  2. 2. T = 110
  3. 3. css = 70.59
  4. 4. K = 9
  5. 5. T(0) = 0.2353
  6. 6. css = 4

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