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)+16GC(s)0.04H+

An amplifier with gain G = 16 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 = 16H = 0.04positive feedback
T =
2.Easy
R(s)+5G₁7G₂C(s)0.5H−

In the block diagram the forward path has the gains G₁ = 5 and G₂ = 7 in series, and the negative feedback path has the gain H = 0.5. Find the overall gain T = C/R.

G₁ = 5G₂ = 7H = 0.5
T =
3.Medium
R(s)+Ks(s + 16)G(s)C(s)−

The plant G(s) = K/(s(s + 16)) 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 + 16))unity negative feedback
K =
4.Medium
R(s)+9(s + 8)(s + 1)(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 9(s + 8)/((s + 1)(s + 5)). A step of size 2 is applied at the reference. Find the steady-state error ess.

G(s) = 9(s + 8)/((s + 1)(s + 5))R = 2
ess =
5.Hard
R(s)+Kcontroller+D(s)+6s + 1plantC(s)−

A proportional controller K drives the plant G(s) = 6/(s + 1) in a unity negative feedback loop. A disturbance step of size 5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 6.

G(s) = 6/(s + 1)D = 5css ≤ 6
K =
6.Hard
R(s)+Kcontroller+D(s)+9s + 1plantC(s)−

A proportional controller K drives the plant G(s) = 9/(s + 1) 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 0.45.

G(s) = 9/(s + 1)D = 1css ≤ 0.45
K =

Answer key

  1. 1. T = 44.44
  2. 2. T = 1.892
  3. 3. K = 64
  4. 4. ess = 0.1299
  5. 5. K = 0.6667
  6. 6. K = 2.111

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