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)+7GC(s)0.04H+

An amplifier with gain G = 7 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 = 7H = 0.04positive feedback
T =
2.Easy
R(s)+6s + 10G(s)C(s)−

A plant G(s) = 6/(s + 10) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 6/(s + 10)unity negative feedback
T(0) =
3.Medium
R(s)+18K+9s + 1G(s)C(s)5H₁−−

The plant G(s) = 9/(s + 1) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 18 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 9/(s + 1)H₁ = 5K = 18
p =
4.Medium
R(s)+5(s + 3)(s + 1)(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 5(s + 3)/((s + 1)(s + 2)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 5(s + 3)/((s + 1)(s + 2))R = 5
ess =
5.Hard
R(s)+14controller+D(s)+1s + 9plantC(s)−

A proportional controller K = 14 drives the plant G(s) = 1/(s + 9) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 5 and a disturbance step of size 0.5 are applied together. Find the steady-state output css.

K = 14G(s) = 1/(s + 9)D = 0.5R = 5
css =
6.Hard
R(s)+Ks(s + 5)(s + 6)G(s)C(s)−

The plant G(s) = K/(s(s + 5)(s + 6)) 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(s + 5)(s + 6))unity negative feedback
Kmax =

Answer key

  1. 1. T = 9.722
  2. 2. T(0) = 0.375
  3. 3. p = −208
  4. 4. ess = 0.5882
  5. 5. css = 3.065
  6. 6. Kmax = 330

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