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)+20G₁7G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 20 and G₂ = 7 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 20G₂ = 7H = 0.25
T =
2.Easy
R(s)+3GC(s)0.1H+

An amplifier with gain G = 3 has positive feedback through a path with gain H = 0.1 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 3H = 0.1positive feedback
T =
3.Medium
R(s)+16K+5s + 4G(s)C(s)2H₁−−

The plant G(s) = 5/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 16 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 5/(s + 4)H₁ = 2K = 16
T(0) =
4.Medium
R(s)+26s + 3G(s)C(s)2H−

A plant G(s) = 26/(s + 3) is controlled in a negative feedback loop whose sensor has the gain H = 2. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 26/(s + 3)H = 2R = 1
css =
5.Hard
R(s)+12s + 3G₁+8s + 6G₂C(s)1H₁−0.25H₂−

Reduce the block diagram with G₁ = 12/(s + 3), G₂ = 8/(s + 6), 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 = 12/(s + 3)G₂ = 8/(s + 6)H₁ = 1H₂ = 0.25
T(0) =
6.Hard
R(s)+12controller+D(s)+3s + 4plantC(s)−

A proportional controller K = 12 drives the plant G(s) = 3/(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 10 and a disturbance step of size 1 are applied together. Find the steady-state output css.

K = 12G(s) = 3/(s + 4)D = 1R = 10
css =

Answer key

  1. 1. T = 3.889
  2. 2. T = 4.286
  3. 3. T(0) = 0.8511
  4. 4. css = 0.4727
  5. 5. T(0) = 1.455
  6. 6. css = 9.075

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