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)+2G₁6G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 2 and G₂ = 6 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 2G₂ = 6H = 0.25
T =
2.Easy
R(s)+7s + 1G(s)C(s)−

A plant G(s) = 7/(s + 1) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 7/(s + 1)unity negative feedback
T(0) =
3.Medium
R(s)+5(s + 2)(s + 4)(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 5(s + 2)/((s + 4)(s + 5)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 5(s + 2)/((s + 4)(s + 5))R = 5
ess =
4.Medium
R(s)+15K+10s + 5G(s)C(s)5H₁−−

The plant G(s) = 10/(s + 5) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 15 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 10/(s + 5)H₁ = 5K = 15
T(0) =
5.Hard
R(s)+18s + 4G₁+2s + 5G₂C(s)1H₁−0.25H₂−

Reduce the block diagram with G₁ = 18/(s + 4), G₂ = 2/(s + 5), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 18/(s + 4)G₂ = 2/(s + 5)H₁ = 1H₂ = 0.25
T(0) =
6.Hard
R(s)+17s + 4G₁+3s + 3G₂C(s)2H₁−1H₂−

Reduce the block diagram with G₁ = 17/(s + 4), G₂ = 3/(s + 3), an inner negative feedback H₁ = 2 around G₂ and an outer negative feedback H₂ = 1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 17/(s + 4)G₂ = 3/(s + 3)H₁ = 2H₂ = 1
T(0) =

Answer key

  1. 1. T = 3
  2. 2. T(0) = 0.875
  3. 3. ess = 3.333
  4. 4. T(0) = 0.7317
  5. 5. T(0) = 0.973
  6. 6. T(0) = 0.5862

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