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)+13GC(s)0.025H+

An amplifier with gain G = 13 has positive feedback through a path with gain H = 0.025 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 13H = 0.025positive feedback
T =
2.Easy
R(s)+9s + 10G(s)C(s)−

A plant G(s) = 9/(s + 10) is placed in a unity negative feedback loop. A step of size 2 is applied at R. Find the steady-state output css.

G(s) = 9/(s + 10)unity negative feedbackR = 2
css =
3.Medium
R(s)+19K+1s + 4G(s)C(s)2H₁−−

The plant G(s) = 1/(s + 4) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 19 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 1/(s + 4)H₁ = 2K = 19
p =
4.Medium
R(s)+11K+5s + 3G(s)C(s)1H₁−−

The plant G(s) = 5/(s + 3) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 11 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 5/(s + 3)H₁ = 1K = 11
T(0) =
5.Hard
R(s)+K(s + 2)(s + 4)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 4)(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 + 2)(s + 4)(s + 8))unity negative feedback
Kmax =
6.Hard
R(s)+K(s + 2)(s + 5)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 5)(s + 7)) 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 + 2)(s + 5)(s + 7))unity negative feedback
Kmax =

Answer key

  1. 1. T = 19.26
  2. 2. css = 0.9474
  3. 3. p = −25
  4. 4. T(0) = 0.873
  5. 5. Kmax = 720
  6. 6. Kmax = 756

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