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)+4GC(s)0.04H+

An amplifier with gain G = 4 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 = 4H = 0.04positive feedback
T =
2.Easy
R(s)8G₂10G₃+−3G₁C(s)

The signal R splits into two parallel blocks G₂ = 8 and G₃ = 10. 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 = 8G₃ = 10signs: + G₂, − G₃
T =
3.Medium
R(s)+K(s + 2)(s + 4)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 4)) 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 + 2)(s + 4))unity negative feedback
K =
4.Medium
R(s)+44s(s + 3)G(s)C(s)−

A unity negative feedback loop has G(s) = 44/(s(s + 3)). The reference is a ramp r(t) = 2·t. Find the steady-state error ess.

G(s) = 44/(s(s + 3))r(t) = 2·t
ess =
5.Hard
R(s)+16s + 4G₁+9s + 3G₂C(s)1H₁−0.1H₂−

Reduce the block diagram with G₁ = 16/(s + 4), G₂ = 9/(s + 3), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 16/(s + 4)G₂ = 9/(s + 3)H₁ = 1H₂ = 0.1
T(0) =
6.Hard
R(s)+22controller+D(s)+9s + 7plantC(s)−

A proportional controller K = 22 drives the plant G(s) = 9/(s + 7) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). With R = 0, a disturbance step of size 1 is applied. Find the steady-state output css.

K = 22G(s) = 9/(s + 7)D = 1R = 0
css =

Answer key

  1. 1. T = 4.762
  2. 2. T = −6
  3. 3. K = 1
  4. 4. ess = 0.1364
  5. 5. T(0) = 2.308
  6. 6. css = 0.0439

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