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)+13G₁1G₂C(s)0.2H−

In the block diagram the forward path has the gains G₁ = 13 and G₂ = 1 in series, and the negative feedback path has the gain H = 0.2. Find the overall gain T = C/R.

G₁ = 13G₂ = 1H = 0.2
T =
2.Easy
R(s)+10GC(s)0.04H+

An amplifier with gain G = 10 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 = 10H = 0.04positive feedback
T =
3.Medium
R(s)+K(s + 2)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 12)) 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 + 12))unity negative feedback
K =
4.Medium
R(s)+19s + 4G(s)C(s)0.5H−

A plant G(s) = 19/(s + 4) is controlled in a negative feedback loop whose sensor has the gain H = 0.5. A step of size 5 is applied at R. Find the steady-state output css.

G(s) = 19/(s + 4)H = 0.5R = 5
css =
5.Hard
R(s)+Kcontroller+D(s)+2s + 7plantC(s)−

A proportional controller K drives the plant G(s) = 2/(s + 7) 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 0.02857.

G(s) = 2/(s + 7)D = 1css ≤ 0.02857
K =
6.Hard
R(s)+2s + 2G₁+2s + 8G₂C(s)2H₁−0.2H₂−

Reduce the block diagram with G₁ = 2/(s + 2), G₂ = 2/(s + 8), an inner negative feedback H₁ = 2 around G₂ and an outer negative feedback H₂ = 0.2. Find the DC gain T(0) of C(s)/R(s).

G₁ = 2/(s + 2)G₂ = 2/(s + 8)H₁ = 2H₂ = 0.2
T(0) =

Answer key

  1. 1. T = 3.611
  2. 2. T = 16.67
  3. 3. K = 25
  4. 4. css = 7.037
  5. 5. K = 31.5
  6. 6. T(0) = 0.1613

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