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)+1s + 9G(s)C(s)−

A plant G(s) = 1/(s + 9) is placed in a unity negative feedback loop. A step of size 5 is applied at R. Find the steady-state output css.

G(s) = 1/(s + 9)unity negative feedbackR = 5
css =
2.Easy
R(s)+11G₁7G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 11 and G₂ = 7 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 11G₂ = 7H = 0.05
T =
3.Medium
R(s)+17s + 8G(s)C(s)0.2H−

A plant G(s) = 17/(s + 8) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.

G(s) = 17/(s + 8)H = 0.2
τ = s
4.Medium
R(s)+K(s + 4)(s + 9)G(s)C(s)−

The plant G(s) = K/((s + 4)(s + 9)) 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 + 4)(s + 9))unity negative feedback
K =
5.Hard
R(s)+4controller+D(s)+6s + 3plantC(s)−

A proportional controller K = 4 drives the plant G(s) = 6/(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 0.5 is applied. Find the steady-state output css.

K = 4G(s) = 6/(s + 3)D = 0.5R = 0
css =
6.Hard
R(s)+Kcontroller+D(s)+6s + 3plantC(s)−

A proportional controller K drives the plant G(s) = 6/(s + 3) 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 0.4.

G(s) = 6/(s + 3)D = 1css ≤ 0.4
K =

Answer key

  1. 1. css = 0.5
  2. 2. T = 15.88
  3. 3. τ = 0.08772 s
  4. 4. K = 6.25
  5. 5. css = 0.1111
  6. 6. K = 2

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