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)+6G₁10G₂C(s)0.5H−

In the block diagram the forward path has the gains G₁ = 6 and G₂ = 10 in series, and the negative feedback path has the gain H = 0.5. Find the overall gain T = C/R.

G₁ = 6G₂ = 10H = 0.5
T =
2.Easy
R(s)+14G₁6G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 14 and G₂ = 6 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 14G₂ = 6H = 0.05
T =
3.Medium
R(s)+20K+6s + 1G(s)C(s)4H₁−−

The plant G(s) = 6/(s + 1) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 20 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 6/(s + 1)H₁ = 4K = 20
T(0) =
4.Medium
R(s)+6s(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 6/(s(s + 4)). The reference is a ramp r(t) = 5·t. Find the steady-state error ess.

G(s) = 6/(s(s + 4))r(t) = 5·t
ess =
5.Hard
R(s)+18s + 5G₁+1s + 4G₂C(s)0.5H₁−1H₂−

Reduce the block diagram with G₁ = 18/(s + 5), G₂ = 1/(s + 4), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 18/(s + 5)G₂ = 1/(s + 4)H₁ = 0.5H₂ = 1
T(0) =
6.Hard
R(s)+4controller+D(s)+5s + 5plantC(s)−

A proportional controller K = 4 drives the plant G(s) = 5/(s + 5) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). With R = 0, a disturbance step of size 1 is applied. Find the steady-state output css.

K = 4G(s) = 5/(s + 5)D = 1R = 0
css =

Answer key

  1. 1. T = 1.935
  2. 2. T = 16.15
  3. 3. T(0) = 0.8276
  4. 4. ess = 3.333
  5. 5. T(0) = 0.4444
  6. 6. css = 0.2

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