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)+16G₁3G₂C(s)0.5H−

In the block diagram the forward path has the gains G₁ = 16 and G₂ = 3 in series, and the negative feedback path has the gain H = 0.5. Find the overall gain T = C/R.

G₁ = 16G₂ = 3H = 0.5
T =
2.Easy
R(s)+20GC(s)0.025H+

An amplifier with gain G = 20 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 = 20H = 0.025positive feedback
T =
3.Medium
R(s)+Ks(s + 11)G(s)C(s)−

The plant G(s) = K/(s(s + 11)) 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 + 11))unity negative feedback
K =
4.Medium
R(s)+Ks(s + 2)G(s)C(s)−

The plant G(s) = K/(s(s + 2)) 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 + 2))unity negative feedback
K =
5.Hard
R(s)+Ks(s + 6)(s + 9)G(s)C(s)−

The plant G(s) = K/(s(s + 6)(s + 9)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/(s(s + 6)(s + 9))unity negative feedback
Kmax =
6.Hard
R(s)+80s(s + 6)G(s)C(s)0.5H−

The plant G(s) = 80/(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) = 80/(s(s + 6))H = 0.5
ωd = rad/s

Answer key

  1. 1. T = 1.92
  2. 2. T = 40
  3. 3. K = 30.25
  4. 4. K = 1
  5. 5. Kmax = 810
  6. 6. ωd = 5.568 rad/s

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