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)+1s + 4G(s)C(s)−

A plant G(s) = 1/(s + 4) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 1/(s + 4)unity negative feedback
τ = s
2.Easy
R(s)+12s + 7G(s)C(s)−

A plant G(s) = 12/(s + 7) is placed in a unity negative feedback loop. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 12/(s + 7)unity negative feedbackR = 1
css =
3.Medium
R(s)+K(s + 7)(s + 11)G(s)C(s)−

The plant G(s) = K/((s + 7)(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 + 7)(s + 11))unity negative feedback
K =
4.Medium
R(s)+K(s + 1)(s + 10)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 10)) 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 + 10))unity negative feedback
K =
5.Hard
R(s)+11s + 4G₁+5s + 4G₂C(s)0.5H₁−0.5H₂−

Reduce the block diagram with G₁ = 11/(s + 4), G₂ = 5/(s + 4), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 11/(s + 4)G₂ = 5/(s + 4)H₁ = 0.5H₂ = 0.5
T(0) =
6.Hard
R(s)+12s + 3G₁+7s + 3G₂C(s)4H₁−0.5H₂−

Reduce the block diagram with G₁ = 12/(s + 3), G₂ = 7/(s + 3), 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 = 12/(s + 3)G₂ = 7/(s + 3)H₁ = 4H₂ = 0.5
T(0) =

Answer key

  1. 1. τ = 0.2 s
  2. 2. css = 0.6316
  3. 3. K = 4
  4. 4. K = 20.25
  5. 5. T(0) = 1.028
  6. 6. T(0) = 0.6222

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