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)+16G₁3G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 16 and G₂ = 3 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 16G₂ = 3H = 0.1
T =
2.Easy
R(s)+7G₁10G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 7 and G₂ = 10 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 7G₂ = 10H = 0.1
T =
3.Medium
R(s)+15K+5s + 6G(s)C(s)2H₁−−

The plant G(s) = 5/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 15 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 5/(s + 6)H₁ = 2K = 15
p =
4.Medium
R(s)+2s + 3G(s)C(s)0.5H−

A plant G(s) = 2/(s + 3) is controlled in a negative feedback loop whose sensor has the gain H = 0.5. Find the time constant τ of the closed loop.

G(s) = 2/(s + 3)H = 0.5
τ = s
5.Hard
R(s)+Kcontroller+D(s)+9s + 9plantC(s)−

A proportional controller K drives the plant G(s) = 9/(s + 9) in a unity negative feedback loop. A disturbance step of size 5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.05.

G(s) = 9/(s + 9)D = 5css ≤ 0.05
K =
6.Hard
R(s)+62s(s + 3)G(s)C(s)1H−

The plant G(s) = 62/(s(s + 3)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 62/(s(s + 3))H = 1
ωd = rad/s

Answer key

  1. 1. T = 8.276
  2. 2. T = 8.75
  3. 3. p = −91
  4. 4. τ = 0.25 s
  5. 5. K = 99
  6. 6. ωd = 7.73 rad/s

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