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)+13G₁6G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 13 and G₂ = 6 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 13G₂ = 6H = 0.25
T =
2.Easy
R(s)+19GC(s)0.04H+

An amplifier with gain G = 19 has positive feedback through a path with gain H = 0.04 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 19H = 0.04positive feedback
T =
3.Medium
R(s)+20K+6s + 4G(s)C(s)5H₁−−

The plant G(s) = 6/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 20 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 6/(s + 4)H₁ = 5K = 20
p =
4.Medium
R(s)+Ks(s + 3)G(s)C(s)−

The plant G(s) = K/(s(s + 3)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).

G(s) = K/(s(s + 3))unity negative feedback
K =
5.Hard
R(s)+14s + 2G₁+3s + 1G₂C(s)1H₁−0.25H₂−

Reduce the block diagram with G₁ = 14/(s + 2), G₂ = 3/(s + 1), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 14/(s + 2)G₂ = 3/(s + 1)H₁ = 1H₂ = 0.25
T(0) =
6.Hard
R(s)+14s(s + 4)G(s)C(s)1H−

The plant G(s) = 14/(s(s + 4)) 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) = 14/(s(s + 4))H = 1
ωd = rad/s

Answer key

  1. 1. T = 3.805
  2. 2. T = 79.17
  3. 3. p = −154
  4. 4. K = 2.25
  5. 5. T(0) = 2.27
  6. 6. ωd = 3.162 rad/s

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