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)2G₂5G₃+−2G₁C(s)

The signal R splits into two parallel blocks G₂ = 2 and G₃ = 5. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 2. Find the overall gain T = C/R.

G₁ = 2G₂ = 2G₃ = 5signs: + G₂, − G₃
T =
2.Easy
R(s)+13GC(s)0.02H+

An amplifier with gain G = 13 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 13H = 0.02positive feedback
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)+12K+1s + 3G(s)C(s)0.5H₁−−

The plant G(s) = 1/(s + 3) has an inner (minor) negative feedback loop with gain H₁ = 0.5. A controller gain K = 12 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 1/(s + 3)H₁ = 0.5K = 12
T(0) =
5.Hard
R(s)+18s + 5G₁+10s + 2G₂C(s)4H₁−0.5H₂−

Reduce the block diagram with G₁ = 18/(s + 5), G₂ = 10/(s + 2), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 18/(s + 5)G₂ = 10/(s + 2)H₁ = 4H₂ = 0.5
T(0) =
6.Hard
R(s)+10controller+D(s)+7s + 7plantC(s)−

A proportional controller K = 10 drives the plant G(s) = 7/(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 0.5 is applied. Find the steady-state output css.

K = 10G(s) = 7/(s + 7)D = 0.5R = 0
css =

Answer key

  1. 1. T = −6
  2. 2. T = 17.57
  3. 3. K = 1
  4. 4. T(0) = 0.7742
  5. 5. T(0) = 0.6
  6. 6. css = 0.04545

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