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)+16s + 6G(s)C(s)−

A plant G(s) = 16/(s + 6) is placed in a unity negative feedback loop. A step of size 10 is applied at R. Find the steady-state output css.

G(s) = 16/(s + 6)unity negative feedbackR = 10
css =
2.Easy
R(s)+8s + 4G(s)C(s)−

A plant G(s) = 8/(s + 4) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 8/(s + 4)unity negative feedback
τ = s
3.Medium
R(s)+7K+10s + 1G(s)C(s)3H₁−−

The plant G(s) = 10/(s + 1) has an inner (minor) negative feedback loop with gain H₁ = 3. A controller gain K = 7 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 10/(s + 1)H₁ = 3K = 7
p =
4.Medium
R(s)+10s(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 10/(s(s + 6)). The reference is a ramp r(t) = 2·t. Find the steady-state error ess.

G(s) = 10/(s(s + 6))r(t) = 2·t
ess =
5.Hard
R(s)+18s(s + 7)G(s)C(s)2H−

The plant G(s) = 18/(s(s + 7)) 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) = 18/(s(s + 7))H = 2
ωd = rad/s
6.Hard
R(s)+64s(s + 2)G(s)C(s)0.5H−

The plant G(s) = 64/(s(s + 2)) 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) = 64/(s(s + 2))H = 0.5
ωd = rad/s

Answer key

  1. 1. css = 7.273
  2. 2. τ = 0.08333 s
  3. 3. p = −101
  4. 4. ess = 1.2
  5. 5. ωd = 4.873 rad/s
  6. 6. ωd = 5.568 rad/s

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