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)+15GC(s)0.025H+

An amplifier with gain G = 15 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 = 15H = 0.025positive feedback
T =
2.Easy
R(s)+2G₁10G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 2 and G₂ = 10 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 2G₂ = 10H = 0.25
T =
3.Medium
R(s)+13s + 7G(s)C(s)0.2H−

A plant G(s) = 13/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 0.2. Find the time constant τ of the closed loop.

G(s) = 13/(s + 7)H = 0.2
τ = s
4.Medium
R(s)+K(s + 3)(s + 6)G(s)C(s)−

The plant G(s) = K/((s + 3)(s + 6)) 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 + 3)(s + 6))unity negative feedback
K =
5.Hard
R(s)+K(s + 5)(s + 7)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 5)(s + 7)(s + 8)) 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 + 5)(s + 7)(s + 8))unity negative feedback
ω = rad/s
6.Hard
R(s)+Kcontroller+D(s)+10s + 2plantC(s)−

A proportional controller K drives the plant G(s) = 10/(s + 2) in a unity negative feedback loop. A disturbance step of size 2 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 2.

G(s) = 10/(s + 2)D = 2css ≤ 2
K =

Answer key

  1. 1. T = 24
  2. 2. T = 3.333
  3. 3. τ = 0.1042 s
  4. 4. K = 2.25
  5. 5. ω = 11.45 rad/s
  6. 6. K = 0.8

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