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)7G₂2G₃++8G₁C(s)

The signal R splits into two parallel blocks G₂ = 7 and G₃ = 2. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 8. Find the overall gain T = C/R.

G₁ = 8G₂ = 7G₃ = 2signs: + G₂, + G₃
T =
2.Easy
R(s)+11s + 1G(s)C(s)−

A plant G(s) = 11/(s + 1) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 11/(s + 1)unity negative feedback
τ = s
3.Medium
R(s)+40s(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 40/(s(s + 9)). The reference is a ramp r(t) = 10·t. Find the steady-state error ess.

G(s) = 40/(s(s + 9))r(t) = 10·t
ess =
4.Medium
R(s)+11s + 7G(s)C(s)2H−

A plant G(s) = 11/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 2. A step of size 2 is applied at R. Find the steady-state output css.

G(s) = 11/(s + 7)H = 2R = 2
css =
5.Hard
R(s)+K(s + 1)(s + 3)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 3)(s + 8)) 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 + 1)(s + 3)(s + 8))unity negative feedback
ω = rad/s
6.Hard
R(s)+K(s + 2)(s + 3)(s + 6)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 3)(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 + 2)(s + 3)(s + 6))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = 72
  2. 2. τ = 0.08333 s
  3. 3. ess = 2.25
  4. 4. css = 0.7586
  5. 5. ω = 5.916 rad/s
  6. 6. ω = 6 rad/s

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