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)+8s + 5G(s)C(s)−

A plant G(s) = 8/(s + 5) is placed in a unity negative feedback loop. A step of size 5 is applied at R. Find the steady-state output css.

G(s) = 8/(s + 5)unity negative feedbackR = 5
css =
2.Easy
R(s)+17GC(s)0.025H+

An amplifier with gain G = 17 has positive feedback through a path with gain H = 0.025 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 17H = 0.025positive feedback
T =
3.Medium
R(s)+6(s + 1)(s + 6)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 6(s + 1)/((s + 6)(s + 9)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 6(s + 1)/((s + 6)(s + 9))R = 5
ess =
4.Medium
R(s)+19s + 8G(s)C(s)0.5H−

A plant G(s) = 19/(s + 8) is controlled in a negative feedback loop whose sensor has the gain H = 0.5. Find the time constant τ of the closed loop.

G(s) = 19/(s + 8)H = 0.5
τ = s
5.Hard
R(s)+26s(s + 6)G(s)C(s)0.5H−

The plant G(s) = 26/(s(s + 6)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 26/(s(s + 6))H = 0.5
ωd = rad/s
6.Hard
R(s)+4controller+D(s)+3s + 4plantC(s)−

A proportional controller K = 4 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). With R = 0, a disturbance step of size 10 is applied. Find the steady-state output css.

K = 4G(s) = 3/(s + 4)D = 10R = 0
css =

Answer key

  1. 1. css = 3.077
  2. 2. T = 29.57
  3. 3. ess = 4.5
  4. 4. τ = 0.05714 s
  5. 5. ωd = 2 rad/s
  6. 6. css = 1.875

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