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)+15s + 10G(s)C(s)−

A plant G(s) = 15/(s + 10) is placed in a unity negative feedback loop. A step of size 5 is applied at R. Find the steady-state output css.

G(s) = 15/(s + 10)unity negative feedbackR = 5
css =
2.Easy
R(s)14G₂10G₃+−2G₁C(s)

The signal R splits into two parallel blocks G₂ = 14 and G₃ = 10. 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 = 14G₃ = 10signs: + G₂, − G₃
T =
3.Medium
R(s)+Ks(s + 16)G(s)C(s)−

The plant G(s) = K/(s(s + 16)) 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 + 16))unity negative feedback
K =
4.Medium
R(s)+K(s + 1)(s + 11)G(s)C(s)−

The plant G(s) = K/((s + 1)(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 + 1)(s + 11))unity negative feedback
K =
5.Hard
R(s)+3s + 2G₁+1s + 5G₂C(s)4H₁−0.5H₂−

Reduce the block diagram with G₁ = 3/(s + 2), G₂ = 1/(s + 5), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 3/(s + 2)G₂ = 1/(s + 5)H₁ = 4H₂ = 0.5
T(0) =
6.Hard
R(s)+Kcontroller+D(s)+9s + 3plantC(s)−

A proportional controller K drives the plant G(s) = 9/(s + 3) 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 0.06.

G(s) = 9/(s + 3)D = 1css ≤ 0.06
K =

Answer key

  1. 1. css = 3
  2. 2. T = 8
  3. 3. K = 64
  4. 4. K = 25
  5. 5. T(0) = 0.1538
  6. 6. K = 16.33

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