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)+3G₁7G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 3 and G₂ = 7 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 3G₂ = 7H = 0.05
T =
2.Easy
R(s)+14GC(s)0.04H+

An amplifier with gain G = 14 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 = 14H = 0.04positive feedback
T =
3.Medium
R(s)+32s + 1G(s)C(s)0.1H−

A plant G(s) = 32/(s + 1) is controlled in a negative feedback loop whose sensor has the gain H = 0.1. A step of size 12 is applied at R. Find the steady-state output css.

G(s) = 32/(s + 1)H = 0.1R = 12
css =
4.Medium
R(s)+K(s + 1)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 1)(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 + 1)(s + 12))unity negative feedback
K =
5.Hard
R(s)+K(s + 4)(s + 5)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 4)(s + 5)(s + 8)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/((s + 4)(s + 5)(s + 8))unity negative feedback
Kmax =
6.Hard
R(s)+14controller+D(s)+2s + 3plantC(s)−

A proportional controller K = 14 drives the plant G(s) = 2/(s + 3) 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 = 14G(s) = 2/(s + 3)D = 1R = 0
css =

Answer key

  1. 1. T = 10.24
  2. 2. T = 31.82
  3. 3. css = 91.43
  4. 4. K = 30.25
  5. 5. Kmax = 1404
  6. 6. css = 0.06452

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