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)+6G₁5G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 6 and G₂ = 5 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 6G₂ = 5H = 0.25
T =
2.Easy
R(s)+2G₁5G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 2 and G₂ = 5 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 2G₂ = 5H = 0.05
T =
3.Medium
R(s)+8s(s + 10)G(s)C(s)−

A unity negative feedback loop has G(s) = 8/(s(s + 10)). The reference is a ramp r(t) = 2·t. Find the steady-state error ess.

G(s) = 8/(s(s + 10))r(t) = 2·t
ess =
4.Medium
R(s)+10(s + 6)(s + 1)(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 10(s + 6)/((s + 1)(s + 5)). A step of size 1 is applied at the reference. Find the steady-state error ess.

G(s) = 10(s + 6)/((s + 1)(s + 5))R = 1
ess =
5.Hard
R(s)+78s(s + 2)G(s)C(s)0.5H−

The plant G(s) = 78/(s(s + 2)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 78/(s(s + 2))H = 0.5
ωd = rad/s
6.Hard
R(s)+72s(s + 6)G(s)C(s)2H−

The plant G(s) = 72/(s(s + 6)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 72/(s(s + 6))H = 2
σ =

Answer key

  1. 1. T = 3.529
  2. 2. T = 6.667
  3. 3. ess = 2.5
  4. 4. ess = 0.07692
  5. 5. ωd = 6.164 rad/s
  6. 6. σ = −3

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