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)+7G₁1G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 7 and G₂ = 1 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 7G₂ = 1H = 0.25
T =
2.Easy
R(s)+20G₁8G₂C(s)0.5H−

In the block diagram the forward path has the gains G₁ = 20 and G₂ = 8 in series, and the negative feedback path has the gain H = 0.5. Find the overall gain T = C/R.

G₁ = 20G₂ = 8H = 0.5
T =
3.Medium
R(s)+7(s + 8)(s + 1)(s + 3)G(s)C(s)−

A unity negative feedback loop has G(s) = 7(s + 8)/((s + 1)(s + 3)). A step of size 2 is applied at the reference. Find the steady-state error ess.

G(s) = 7(s + 8)/((s + 1)(s + 3))R = 2
ess =
4.Medium
R(s)+20s + 3G(s)C(s)0.2H−

A plant G(s) = 20/(s + 3) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.

G(s) = 20/(s + 3)H = 0.2
τ = s
5.Hard
R(s)+19s + 4G₁+7s + 7G₂C(s)1H₁−0.5H₂−

Reduce the block diagram with G₁ = 19/(s + 4), G₂ = 7/(s + 7), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.5. Find the DC gain T(0) of C(s)/R(s).

G₁ = 19/(s + 4)G₂ = 7/(s + 7)H₁ = 1H₂ = 0.5
T(0) =
6.Hard
R(s)+K(s + 4)(s + 6)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 4)(s + 6)(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 + 4)(s + 6)(s + 8))unity negative feedback
Kmax =

Answer key

  1. 1. T = 2.545
  2. 2. T = 1.975
  3. 3. ess = 0.1017
  4. 4. τ = 0.1429 s
  5. 5. T(0) = 1.086
  6. 6. Kmax = 1680

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