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)10G₂8G₃+−9G₁C(s)

The signal R splits into two parallel blocks G₂ = 10 and G₃ = 8. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 9. Find the overall gain T = C/R.

G₁ = 9G₂ = 10G₃ = 8signs: + G₂, − G₃
T =
2.Easy
R(s)+16GC(s)0.025H+

An amplifier with gain G = 16 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 = 16H = 0.025positive feedback
T =
3.Medium
R(s)+Ks(s + 20)G(s)C(s)−

The plant G(s) = K/(s(s + 20)) 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(s + 20))unity negative feedback
K =
4.Medium
R(s)+K(s + 2)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 12)) 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 + 2)(s + 12))unity negative feedback
K =
5.Hard
R(s)+40s(s + 11)G(s)C(s)1H−

The plant G(s) = 40/(s(s + 11)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 40/(s(s + 11))H = 1
ωd = rad/s
6.Hard
R(s)+4s + 5G₁+7s + 7G₂C(s)4H₁−0.2H₂−

Reduce the block diagram with G₁ = 4/(s + 5), G₂ = 7/(s + 7), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.2. Find the DC gain T(0) of C(s)/R(s).

G₁ = 4/(s + 5)G₂ = 7/(s + 7)H₁ = 4H₂ = 0.2
T(0) =

Answer key

  1. 1. T = 18
  2. 2. T = 26.67
  3. 3. K = 100
  4. 4. K = 25
  5. 5. ωd = 3.122 rad/s
  6. 6. T(0) = 0.155

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