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)9G₂4G₃++6G₁C(s)

The signal R splits into two parallel blocks G₂ = 9 and G₃ = 4. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 6. Find the overall gain T = C/R.

G₁ = 6G₂ = 9G₃ = 4signs: + G₂, + G₃
T =
2.Easy
R(s)+13GC(s)0.025H+

An amplifier with gain G = 13 has positive feedback through a path with gain H = 0.025 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 13H = 0.025positive feedback
T =
3.Medium
R(s)+20s(s + 4)G(s)C(s)−

A unity negative feedback loop has G(s) = 20/(s(s + 4)). The reference is a ramp r(t) = 10·t. Find the steady-state error ess.

G(s) = 20/(s(s + 4))r(t) = 10·t
ess =
4.Medium
R(s)+8s + 7G(s)C(s)0.1H−

A plant G(s) = 8/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 0.1. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 8/(s + 7)H = 0.1R = 1
css =
5.Hard
R(s)+Ks(s + 1)(s + 6)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(s + 6)) 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(s + 1)(s + 6))unity negative feedback
Kmax =
6.Hard
R(s)+6s + 1G₁+9s + 8G₂C(s)4H₁−0.5H₂−

Reduce the block diagram with G₁ = 6/(s + 1), G₂ = 9/(s + 8), 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 = 6/(s + 1)G₂ = 9/(s + 8)H₁ = 4H₂ = 0.5
T(0) =

Answer key

  1. 1. T = 78
  2. 2. T = 19.26
  3. 3. ess = 2
  4. 4. css = 1.026
  5. 5. Kmax = 42
  6. 6. T(0) = 0.7606

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