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)+9G₁10G₂C(s)1H−

In the block diagram the forward path has the gains G₁ = 9 and G₂ = 10 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 9G₂ = 10H = 1
T =
2.Easy
R(s)7G₂7G₃++2G₁C(s)

The signal R splits into two parallel blocks G₂ = 7 and G₃ = 7. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 2. Find the overall gain T = C/R.

G₁ = 2G₂ = 7G₃ = 7signs: + G₂, + G₃
T =
3.Medium
R(s)+40s + 7G(s)C(s)0.2H−

A plant G(s) = 40/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. A step of size 5 is applied at R. Find the steady-state output css.

G(s) = 40/(s + 7)H = 0.2R = 5
css =
4.Medium
R(s)+17s + 1G(s)C(s)0.2H−

A plant G(s) = 17/(s + 1) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.

G(s) = 17/(s + 1)H = 0.2
τ = s
5.Hard
R(s)+15s + 5G₁+8s + 8G₂C(s)4H₁−0.25H₂−

Reduce the block diagram with G₁ = 15/(s + 5), G₂ = 8/(s + 8), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 15/(s + 5)G₂ = 8/(s + 8)H₁ = 4H₂ = 0.25
T(0) =
6.Hard
R(s)+8s + 5G₁+10s + 5G₂C(s)1H₁−0.2H₂−

Reduce the block diagram with G₁ = 8/(s + 5), G₂ = 10/(s + 5), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.2. Find the DC gain T(0) of C(s)/R(s).

G₁ = 8/(s + 5)G₂ = 10/(s + 5)H₁ = 1H₂ = 0.2
T(0) =

Answer key

  1. 1. T = 0.989
  2. 2. T = 28
  3. 3. css = 13.33
  4. 4. τ = 0.2273 s
  5. 5. T(0) = 0.5217
  6. 6. T(0) = 0.8791

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