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)+12GC(s)0.025H+

An amplifier with gain G = 12 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 = 12H = 0.025positive feedback
T =
2.Easy
R(s)+14GC(s)0.05H+

An amplifier with gain G = 14 has positive feedback through a path with gain H = 0.05 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 14H = 0.05positive feedback
T =
3.Medium
R(s)+50s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 50/(s(s + 8)). The reference is a ramp r(t) = 5·t. Find the steady-state error ess.

G(s) = 50/(s(s + 8))r(t) = 5·t
ess =
4.Medium
R(s)+Ks(s + 8)G(s)C(s)−

The plant G(s) = K/(s(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(s + 8))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+3s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 3/(s + 4) in a unity negative feedback loop. A disturbance step of size 1 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.015.

G(s) = 3/(s + 4)D = 1css ≤ 0.015
K =
6.Hard
R(s)+19s + 2G₁+1s + 5G₂C(s)2H₁−0.5H₂−

Reduce the block diagram with G₁ = 19/(s + 2), G₂ = 1/(s + 5), an inner negative feedback H₁ = 2 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 19/(s + 2)G₂ = 1/(s + 5)H₁ = 2H₂ = 0.5
T(0) =

Answer key

  1. 1. T = 17.14
  2. 2. T = 46.67
  3. 3. ess = 0.8
  4. 4. K = 16
  5. 5. K = 65.33
  6. 6. T(0) = 0.8085

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