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)+8s + 2G(s)C(s)−

A plant G(s) = 8/(s + 2) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 8/(s + 2)unity negative feedback
τ = s
2.Easy
R(s)8G₂11G₃++5G₁C(s)

The signal R splits into two parallel blocks G₂ = 8 and G₃ = 11. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 5. Find the overall gain T = C/R.

G₁ = 5G₂ = 8G₃ = 11signs: + G₂, + G₃
T =
3.Medium
R(s)+44s(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 44/(s(s + 8)). The reference is a ramp r(t) = 2·t. Find the steady-state error ess.

G(s) = 44/(s(s + 8))r(t) = 2·t
ess =
4.Medium
R(s)+17K+6s + 8G(s)C(s)1H₁−−

The plant G(s) = 6/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 17 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 6/(s + 8)H₁ = 1K = 17
T(0) =
5.Hard
R(s)+78s(s + 7)G(s)C(s)1H−

The plant G(s) = 78/(s(s + 7)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 78/(s(s + 7))H = 1
σ =
6.Hard
R(s)+70s(s + 4)G(s)C(s)0.5H−

The plant G(s) = 70/(s(s + 4)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their real part σ.

G(s) = 70/(s(s + 4))H = 0.5
σ =

Answer key

  1. 1. τ = 0.1 s
  2. 2. T = 95
  3. 3. ess = 0.3636
  4. 4. T(0) = 0.8793
  5. 5. σ = −3.5
  6. 6. σ = −2

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