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)+3G₁1G₂C(s)0.2H−

In the block diagram the forward path has the gains G₁ = 3 and G₂ = 1 in series, and the negative feedback path has the gain H = 0.2. Find the overall gain T = C/R.

G₁ = 3G₂ = 1H = 0.2
T =
2.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 =
3.Medium
R(s)+K(s + 8)(s + 11)G(s)C(s)−

The plant G(s) = K/((s + 8)(s + 11)) 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 + 8)(s + 11))unity negative feedback
K =
4.Medium
R(s)+10(s + 6)(s + 1)(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 10(s + 6)/((s + 1)(s + 5)). A step of size 2 is applied at the reference. Find the steady-state error ess.

G(s) = 10(s + 6)/((s + 1)(s + 5))R = 2
ess =
5.Hard
R(s)+13s + 1G₁+10s + 7G₂C(s)0.5H₁−0.25H₂−

Reduce the block diagram with G₁ = 13/(s + 1), G₂ = 10/(s + 7), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 13/(s + 1)G₂ = 10/(s + 7)H₁ = 0.5H₂ = 0.25
T(0) =
6.Hard
R(s)+Kcontroller+D(s)+8s + 5plantC(s)−

A proportional controller K drives the plant G(s) = 8/(s + 5) in a unity negative feedback loop. A disturbance step of size 0.5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.04.

G(s) = 8/(s + 5)D = 0.5css ≤ 0.04
K =

Answer key

  1. 1. T = 1.875
  2. 2. T = 0.989
  3. 3. K = 2.25
  4. 4. ess = 0.1538
  5. 5. T(0) = 2.921
  6. 6. K = 11.88

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