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)3G₂8G₃+−7G₁C(s)

The signal R splits into two parallel blocks G₂ = 3 and G₃ = 8. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 7. Find the overall gain T = C/R.

G₁ = 7G₂ = 3G₃ = 8signs: + G₂, − G₃
T =
2.Easy
R(s)13G₂1G₃++4G₁C(s)

The signal R splits into two parallel blocks G₂ = 13 and G₃ = 1. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 4. Find the overall gain T = C/R.

G₁ = 4G₂ = 13G₃ = 1signs: + G₂, + G₃
T =
3.Medium
R(s)+7(s + 7)(s + 4)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 7(s + 7)/((s + 4)(s + 9)). A step of size 10 is applied at the reference. Find the steady-state error ess.

G(s) = 7(s + 7)/((s + 4)(s + 9))R = 10
ess =
4.Medium
R(s)+3K+3s + 7G(s)C(s)5H₁−−

The plant G(s) = 3/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 5. A controller gain K = 3 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 3/(s + 7)H₁ = 5K = 3
T(0) =
5.Hard
R(s)+K(s + 1)(s + 3)(s + 6)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 3)(s + 6)) 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 + 1)(s + 3)(s + 6))unity negative feedback
ω = rad/s
6.Hard
R(s)+Ks(s + 4)(s + 10)G(s)C(s)−

The plant G(s) = K/(s(s + 4)(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 + 4)(s + 10))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = −35
  2. 2. T = 56
  3. 3. ess = 4.235
  4. 4. T(0) = 0.2903
  5. 5. ω = 5.196 rad/s
  6. 6. ω = 6.325 rad/s

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