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)+12GC(s)0.05H+

An amplifier with gain G = 12 has positive feedback through a path with gain H = 0.05 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 12H = 0.05positive feedback
T =
2.Easy
R(s)2G₂1G₃+−7G₁C(s)

The signal R splits into two parallel blocks G₂ = 2 and G₃ = 1. 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 = 2G₃ = 1signs: + G₂, − G₃
T =
3.Medium
R(s)+9s + 7G(s)C(s)0.5H−

A plant G(s) = 9/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 0.5. Find the time constant τ of the closed loop.

G(s) = 9/(s + 7)H = 0.5
τ = s
4.Medium
R(s)+46s(s + 7)G(s)C(s)−

A unity negative feedback loop has G(s) = 46/(s(s + 7)). The reference is a ramp r(t) = 1·t. Find the steady-state error ess.

G(s) = 46/(s(s + 7))r(t) = 1·t
ess =
5.Hard
R(s)+Ks(s + 5)(s + 6)G(s)C(s)−

The plant G(s) = K/(s(s + 5)(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(s + 5)(s + 6))unity negative feedback
ω = rad/s
6.Hard
R(s)+56s(s + 7)G(s)C(s)0.5H−

The plant G(s) = 56/(s(s + 7)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 56/(s(s + 7))H = 0.5
ωd = rad/s

Answer key

  1. 1. T = 30
  2. 2. T = 7
  3. 3. τ = 0.08696 s
  4. 4. ess = 0.1522
  5. 5. ω = 5.477 rad/s
  6. 6. ωd = 3.969 rad/s

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