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)+16GC(s)0.05H+

An amplifier with gain G = 16 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 = 16H = 0.05positive feedback
T =
2.Easy
R(s)+5s + 3G(s)C(s)−

A plant G(s) = 5/(s + 3) is placed in a unity negative feedback loop. A step of size 5 is applied at R. Find the steady-state output css.

G(s) = 5/(s + 3)unity negative feedbackR = 5
css =
3.Medium
R(s)+48s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 48/(s(s + 2)). The reference is a ramp r(t) = 10·t. Find the steady-state error ess.

G(s) = 48/(s(s + 2))r(t) = 10·t
ess =
4.Medium
R(s)+34s + 5G(s)C(s)0.25H−

A plant G(s) = 34/(s + 5) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. A step of size 5 is applied at R. Find the steady-state output css.

G(s) = 34/(s + 5)H = 0.25R = 5
css =
5.Hard
R(s)+64s(s + 6)G(s)C(s)0.5H−

The plant G(s) = 64/(s(s + 6)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their real part σ.

G(s) = 64/(s(s + 6))H = 0.5
σ =
6.Hard
R(s)+Ks(s + 1)(s + 5)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(s + 5)) 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 + 5))unity negative feedback
ω = rad/s

Answer key

  1. 1. T = 80
  2. 2. css = 3.125
  3. 3. ess = 0.4167
  4. 4. css = 12.59
  5. 5. σ = −3
  6. 6. ω = 2.236 rad/s

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