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)+2GC(s)0.2H+

An amplifier with gain G = 2 has positive feedback through a path with gain H = 0.2 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 2H = 0.2positive feedback
T =
2.Easy
R(s)+13s + 2G(s)C(s)−

A plant G(s) = 13/(s + 2) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 13/(s + 2)unity negative feedback
τ = s
3.Medium
R(s)+14s + 7G(s)C(s)2H−

A plant G(s) = 14/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 2. Find the time constant τ of the closed loop.

G(s) = 14/(s + 7)H = 2
τ = s
4.Medium
R(s)+4(s + 7)(s + 4)(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 4(s + 7)/((s + 4)(s + 6)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 4(s + 7)/((s + 4)(s + 6))R = 5
ess =
5.Hard
R(s)+56s(s + 5)G(s)C(s)2H−

The plant G(s) = 56/(s(s + 5)) 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) = 56/(s(s + 5))H = 2
ωd = rad/s
6.Hard
R(s)+16s(s + 4)G(s)C(s)0.5H−

The plant G(s) = 16/(s(s + 4)) 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) = 16/(s(s + 4))H = 0.5
ωd = rad/s

Answer key

  1. 1. T = 3.333
  2. 2. τ = 0.06667 s
  3. 3. τ = 0.02857 s
  4. 4. ess = 2.308
  5. 5. ωd = 10.28 rad/s
  6. 6. ωd = 2 rad/s

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