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)5G₂5G₃++6G₁C(s)

The signal R splits into two parallel blocks G₂ = 5 and G₃ = 5. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 6. Find the overall gain T = C/R.

G₁ = 6G₂ = 5G₃ = 5signs: + G₂, + G₃
T =
2.Easy
R(s)+14G₁8G₂C(s)0.2H−

In the block diagram the forward path has the gains G₁ = 14 and G₂ = 8 in series, and the negative feedback path has the gain H = 0.2. Find the overall gain T = C/R.

G₁ = 14G₂ = 8H = 0.2
T =
3.Medium
R(s)+16s + 7G(s)C(s)2H−

A plant G(s) = 16/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 2. A step of size 10 is applied at R. Find the steady-state output css.

G(s) = 16/(s + 7)H = 2R = 10
css =
4.Medium
R(s)+K(s + 3)(s + 5)G(s)C(s)−

The plant G(s) = K/((s + 3)(s + 5)) 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 + 3)(s + 5))unity negative feedback
K =
5.Hard
R(s)+18s + 3G₁+7s + 5G₂C(s)2H₁−0.5H₂−

Reduce the block diagram with G₁ = 18/(s + 3), G₂ = 7/(s + 5), an inner negative feedback H₁ = 2 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 18/(s + 3)G₂ = 7/(s + 5)H₁ = 2H₂ = 0.5
T(0) =
6.Hard
R(s)+5controller+D(s)+5s + 4plantC(s)−

A proportional controller K = 5 drives the plant G(s) = 5/(s + 4) 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 10 are applied together. Find the steady-state output css.

K = 5G(s) = 5/(s + 4)D = 10R = 5
css =

Answer key

  1. 1. T = 60
  2. 2. T = 4.786
  3. 3. css = 4.103
  4. 4. K = 1
  5. 5. T(0) = 1.05
  6. 6. css = 6.034

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