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)+13s + 1G(s)C(s)−

A plant G(s) = 13/(s + 1) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 13/(s + 1)unity negative feedback
T(0) =
2.Easy
R(s)15G₂4G₃+−2G₁C(s)

The signal R splits into two parallel blocks G₂ = 15 and G₃ = 4. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 2. Find the overall gain T = C/R.

G₁ = 2G₂ = 15G₃ = 4signs: + G₂, − G₃
T =
3.Medium
R(s)+9(s + 5)(s + 4)(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 9(s + 5)/((s + 4)(s + 6)). A step of size 2 is applied at the reference. Find the steady-state error ess.

G(s) = 9(s + 5)/((s + 4)(s + 6))R = 2
ess =
4.Medium
R(s)+11K+2s + 8G(s)C(s)2H₁−−

The plant G(s) = 2/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 11 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 2/(s + 8)H₁ = 2K = 11
p =
5.Hard
R(s)+28controller+D(s)+2s + 9plantC(s)−

A proportional controller K = 28 drives the plant G(s) = 2/(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 1 and a disturbance step of size 0.5 are applied together. Find the steady-state output css.

K = 28G(s) = 2/(s + 9)D = 0.5R = 1
css =
6.Hard
R(s)+K(s + 4)(s + 5)(s + 6)G(s)C(s)−

The plant G(s) = K/((s + 4)(s + 5)(s + 6)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/((s + 4)(s + 5)(s + 6))unity negative feedback
ω = rad/s

Answer key

  1. 1. T(0) = 0.9286
  2. 2. T = 22
  3. 3. ess = 0.6957
  4. 4. p = −34
  5. 5. css = 0.8769
  6. 6. ω = 8.602 rad/s

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