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)+14GC(s)0.025H+

An amplifier with gain G = 14 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 = 14H = 0.025positive feedback
T =
2.Easy
R(s)5G₂10G₃+−10G₁C(s)

The signal R splits into two parallel blocks G₂ = 5 and G₃ = 10. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 10. Find the overall gain T = C/R.

G₁ = 10G₂ = 5G₃ = 10signs: + G₂, − G₃
T =
3.Medium
R(s)+K(s + 5)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 5)(s + 8)) 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 + 5)(s + 8))unity negative feedback
K =
4.Medium
R(s)+17K+10s + 8G(s)C(s)2H₁−−

The plant G(s) = 10/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 17 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 10/(s + 8)H₁ = 2K = 17
p =
5.Hard
R(s)+Ks(s + 1)(s + 4)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(s + 4)) 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 + 1)(s + 4))unity negative feedback
Kmax =
6.Hard
R(s)+9controller+D(s)+8s + 1plantC(s)−

A proportional controller K = 9 drives the plant G(s) = 8/(s + 1) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 10 and a disturbance step of size 5 are applied together. Find the steady-state output css.

K = 9G(s) = 8/(s + 1)D = 5R = 10
css =

Answer key

  1. 1. T = 21.54
  2. 2. T = −50
  3. 3. K = 2.25
  4. 4. p = −198
  5. 5. Kmax = 20
  6. 6. css = 10.41

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