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)+13G₁4G₂C(s)0.5H−

In the block diagram the forward path has the gains G₁ = 13 and G₂ = 4 in series, and the negative feedback path has the gain H = 0.5. Find the overall gain T = C/R.

G₁ = 13G₂ = 4H = 0.5
T =
2.Easy
R(s)+7s + 6G(s)C(s)−

A plant G(s) = 7/(s + 6) is placed in a unity negative feedback loop. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 7/(s + 6)unity negative feedbackR = 1
css =
3.Medium
R(s)+5K+7s + 5G(s)C(s)4H₁−−

The plant G(s) = 7/(s + 5) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 5 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 7/(s + 5)H₁ = 4K = 5
p =
4.Medium
R(s)+Ks(s + 15)G(s)C(s)−

The plant G(s) = K/(s(s + 15)) 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 + 15))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+7s + 2plantC(s)−

A proportional controller K drives the plant G(s) = 7/(s + 2) 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 1.75.

G(s) = 7/(s + 2)D = 5css ≤ 1.75
K =
6.Hard
R(s)+70s(s + 6)G(s)C(s)1H−

The plant G(s) = 70/(s(s + 6)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 70/(s(s + 6))H = 1
σ =

Answer key

  1. 1. T = 1.926
  2. 2. css = 0.5385
  3. 3. p = −68
  4. 4. K = 56.25
  5. 5. K = 2.571
  6. 6. σ = −3

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