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)+17G₁2G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 17 and G₂ = 2 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 17G₂ = 2H = 0.1
T =
2.Easy
R(s)+19G₁9G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 19 and G₂ = 9 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 19G₂ = 9H = 0.1
T =
3.Medium
R(s)+2K+9s + 6G(s)C(s)1H₁−−

The plant G(s) = 9/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 2 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 9/(s + 6)H₁ = 1K = 2
T(0) =
4.Medium
R(s)+Ks(s + 8)G(s)C(s)−

The plant G(s) = K/(s(s + 8)) 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(s + 8))unity negative feedback
K =
5.Hard
R(s)+K(s + 1)(s + 2)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 2)(s + 8)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/((s + 1)(s + 2)(s + 8))unity negative feedback
Kmax =
6.Hard
R(s)+Kcontroller+D(s)+3s + 8plantC(s)−

A proportional controller K drives the plant G(s) = 3/(s + 8) in a unity negative feedback loop. A disturbance step of size 1 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.00375.

G(s) = 3/(s + 8)D = 1css ≤ 0.00375
K =

Answer key

  1. 1. T = 7.727
  2. 2. T = 9.448
  3. 3. T(0) = 0.5455
  4. 4. K = 16
  5. 5. Kmax = 270
  6. 6. K = 264

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