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)+15G₁1G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 15 and G₂ = 1 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 15G₂ = 1H = 0.05
T =
2.Easy
R(s)+19G₁3G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 19 and G₂ = 3 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 19G₂ = 3H = 0.25
T =
3.Medium
R(s)+1(s + 5)(s + 7)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 1(s + 5)/((s + 7)(s + 9)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 1(s + 5)/((s + 7)(s + 9))R = 5
ess =
4.Medium
R(s)+K(s + 10)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 10)(s + 12)) is in a unity negative feedback loop. Find the gain K for which the closed loop is critically damped (two equal real poles).

G(s) = K/((s + 10)(s + 12))unity negative feedback
K =
5.Hard
R(s)+9s + 5G₁+8s + 1G₂C(s)0.5H₁−1H₂−

Reduce the block diagram with G₁ = 9/(s + 5), G₂ = 8/(s + 1), 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 = 9/(s + 5)G₂ = 8/(s + 1)H₁ = 0.5H₂ = 1
T(0) =
6.Hard
R(s)+10controller+D(s)+9s + 6plantC(s)−

A proportional controller K = 10 drives the plant G(s) = 9/(s + 6) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 10 and a disturbance step of size 2 are applied together. Find the steady-state output css.

K = 10G(s) = 9/(s + 6)D = 2R = 10
css =

Answer key

  1. 1. T = 8.571
  2. 2. T = 3.738
  3. 3. ess = 4.632
  4. 4. K = 1
  5. 5. T(0) = 0.7423
  6. 6. css = 9.563

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