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)+6GC(s)0.05H+

An amplifier with gain G = 6 has positive feedback through a path with gain H = 0.05 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 6H = 0.05positive feedback
T =
2.Easy
R(s)+12s + 5G(s)C(s)−

A plant G(s) = 12/(s + 5) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 12/(s + 5)unity negative feedback
τ = s
3.Medium
R(s)+17K+9s + 3G(s)C(s)1H₁−−

The plant G(s) = 9/(s + 3) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 17 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 9/(s + 3)H₁ = 1K = 17
T(0) =
4.Medium
R(s)+10s + 3G(s)C(s)0.2H−

A plant G(s) = 10/(s + 3) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. A step of size 10 is applied at R. Find the steady-state output css.

G(s) = 10/(s + 3)H = 0.2R = 10
css =
5.Hard
R(s)+78s(s + 4)G(s)C(s)2H−

The plant G(s) = 78/(s(s + 4)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 78/(s(s + 4))H = 2
ωd = rad/s
6.Hard
R(s)+20controller+D(s)+6s + 6plantC(s)−

A proportional controller K = 20 drives the plant G(s) = 6/(s + 6) 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 = 20G(s) = 6/(s + 6)D = 10R = 0
css =

Answer key

  1. 1. T = 8.571
  2. 2. τ = 0.05882 s
  3. 3. T(0) = 0.9273
  4. 4. css = 20
  5. 5. ωd = 12.33 rad/s
  6. 6. css = 0.4762

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