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)7G₂1G₃+−5G₁C(s)

The signal R splits into two parallel blocks G₂ = 7 and G₃ = 1. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 5. Find the overall gain T = C/R.

G₁ = 5G₂ = 7G₃ = 1signs: + G₂, − G₃
T =
2.Easy
R(s)+3GC(s)0.2H+

An amplifier with gain G = 3 has positive feedback through a path with gain H = 0.2 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 3H = 0.2positive feedback
T =
3.Medium
R(s)+1(s + 7)(s + 3)(s + 5)G(s)C(s)−

A unity negative feedback loop has G(s) = 1(s + 7)/((s + 3)(s + 5)). A step of size 10 is applied at the reference. Find the steady-state error ess.

G(s) = 1(s + 7)/((s + 3)(s + 5))R = 10
ess =
4.Medium
R(s)+9(s + 8)(s + 2)(s + 7)G(s)C(s)−

A unity negative feedback loop has G(s) = 9(s + 8)/((s + 2)(s + 7)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 9(s + 8)/((s + 2)(s + 7))R = 5
ess =
5.Hard
R(s)+Ks(s + 1)(s + 10)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(s + 10)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/(s(s + 1)(s + 10))unity negative feedback
ω = rad/s
6.Hard
R(s)+Ks(s + 2)(s + 10)G(s)C(s)−

The plant G(s) = K/(s(s + 2)(s + 10)) 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 + 2)(s + 10))unity negative feedback
Kmax =

Answer key

  1. 1. T = 30
  2. 2. T = 7.5
  3. 3. ess = 6.818
  4. 4. ess = 0.814
  5. 5. ω = 3.162 rad/s
  6. 6. Kmax = 240

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