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)11G₂10G₃++7G₁C(s)

The signal R splits into two parallel blocks G₂ = 11 and G₃ = 10. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 7. Find the overall gain T = C/R.

G₁ = 7G₂ = 11G₃ = 10signs: + G₂, + G₃
T =
2.Easy
R(s)+3GC(s)0.1H+

An amplifier with gain G = 3 has positive feedback through a path with gain H = 0.1 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 3H = 0.1positive feedback
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)+K(s + 5)(s + 11)G(s)C(s)−

The plant G(s) = K/((s + 5)(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 + 5)(s + 11))unity negative feedback
K =
5.Hard
R(s)+6controller+D(s)+2s + 1plantC(s)−

A proportional controller K = 6 drives the plant G(s) = 2/(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 1 are applied together. Find the steady-state output css.

K = 6G(s) = 2/(s + 1)D = 1R = 10
css =
6.Hard
R(s)+80s(s + 4)G(s)C(s)0.5H−

The plant G(s) = 80/(s(s + 4)) 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 + 4))H = 0.5
ωd = rad/s

Answer key

  1. 1. T = 147
  2. 2. T = 4.286
  3. 3. K = 2.25
  4. 4. K = 9
  5. 5. css = 9.385
  6. 6. ωd = 6 rad/s

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