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)+20GC(s)0.01H+

An amplifier with gain G = 20 has positive feedback through a path with gain H = 0.01 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 20H = 0.01positive feedback
T =
2.Easy
R(s)4G₂7G₃+−3G₁C(s)

The signal R splits into two parallel blocks G₂ = 4 and G₃ = 7. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 3. Find the overall gain T = C/R.

G₁ = 3G₂ = 4G₃ = 7signs: + G₂, − G₃
T =
3.Medium
R(s)+K(s + 6)(s + 9)G(s)C(s)−

The plant G(s) = K/((s + 6)(s + 9)) 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 + 6)(s + 9))unity negative feedback
K =
4.Medium
R(s)+28s + 8G(s)C(s)0.1H−

A plant G(s) = 28/(s + 8) is controlled in a negative feedback loop whose sensor has the gain H = 0.1. A step of size 12 is applied at R. Find the steady-state output css.

G(s) = 28/(s + 8)H = 0.1R = 12
css =
5.Hard
R(s)+12s(s + 4)G(s)C(s)2H−

The plant G(s) = 12/(s(s + 4)) 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) = 12/(s(s + 4))H = 2
ωd = rad/s
6.Hard
R(s)+Ks(s + 2)(s + 10)G(s)C(s)−

The plant G(s) = K/(s(s + 2)(s + 10)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/(s(s + 2)(s + 10))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = 25
  2. 2. T = −9
  3. 3. K = 2.25
  4. 4. css = 31.11
  5. 5. ωd = 4.472 rad/s
  6. 6. ω = 4.472 rad/s

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