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)+18G₁10G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 18 and G₂ = 10 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 18G₂ = 10H = 0.1
T =
2.Easy
R(s)2G₂11G₃+−3G₁C(s)

The signal R splits into two parallel blocks G₂ = 2 and G₃ = 11. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 3. Find the overall gain T = C/R.

G₁ = 3G₂ = 2G₃ = 11signs: + G₂, − G₃
T =
3.Medium
R(s)+28s + 5G(s)C(s)0.25H−

A plant G(s) = 28/(s + 5) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. Find the time constant τ of the closed loop.

G(s) = 28/(s + 5)H = 0.25
τ = s
4.Medium
R(s)+3s + 7G(s)C(s)2H−

A plant G(s) = 3/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 2. Find the time constant τ of the closed loop.

G(s) = 3/(s + 7)H = 2
τ = s
5.Hard
R(s)+Ks(s + 1)(s + 7)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(s + 7)) 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(s + 1)(s + 7))unity negative feedback
ω = rad/s
6.Hard
R(s)+10controller+D(s)+6s + 2plantC(s)−

A proportional controller K = 10 drives the plant G(s) = 6/(s + 2) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). With R = 0, a disturbance step of size 2 is applied. Find the steady-state output css.

K = 10G(s) = 6/(s + 2)D = 2R = 0
css =

Answer key

  1. 1. T = 9.474
  2. 2. T = −27
  3. 3. τ = 0.08333 s
  4. 4. τ = 0.07692 s
  5. 5. ω = 2.646 rad/s
  6. 6. css = 0.1935

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