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)+12G₁6G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 12 and G₂ = 6 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 12G₂ = 6H = 0.25
T =
2.Easy
R(s)+17G₁7G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 17 and G₂ = 7 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 17G₂ = 7H = 0.1
T =
3.Medium
R(s)+20K+6s + 1G(s)C(s)4H₁−−

The plant G(s) = 6/(s + 1) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 20 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 6/(s + 1)H₁ = 4K = 20
T(0) =
4.Medium
R(s)+18K+10s + 8G(s)C(s)4H₁−−

The plant G(s) = 10/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 18 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 10/(s + 8)H₁ = 4K = 18
T(0) =
5.Hard
R(s)+30s(s + 7)G(s)C(s)1H−

The plant G(s) = 30/(s(s + 7)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 30/(s(s + 7))H = 1
ωd = rad/s
6.Hard
R(s)+6controller+D(s)+4s + 7plantC(s)−

A proportional controller K = 6 drives the plant G(s) = 4/(s + 7) 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 10 is applied. Find the steady-state output css.

K = 6G(s) = 4/(s + 7)D = 10R = 0
css =

Answer key

  1. 1. T = 3.789
  2. 2. T = 9.225
  3. 3. T(0) = 0.8276
  4. 4. T(0) = 0.7895
  5. 5. ωd = 4.213 rad/s
  6. 6. css = 1.29

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