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)+12s + 9G(s)C(s)−

A plant G(s) = 12/(s + 9) 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) = 12/(s + 9)unity negative feedbackR = 5
css =
2.Easy
R(s)+14GC(s)0.05H+

An amplifier with gain G = 14 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 = 14H = 0.05positive feedback
T =
3.Medium
R(s)+33s + 8G(s)C(s)2H−

A plant G(s) = 33/(s + 8) is controlled in a negative feedback loop whose sensor has the gain H = 2. Find the time constant τ of the closed loop.

G(s) = 33/(s + 8)H = 2
τ = s
4.Medium
R(s)+K(s + 1)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 7)) 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 + 1)(s + 7))unity negative feedback
K =
5.Hard
R(s)+Ks(s + 1)(s + 4)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(s + 4)) 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 + 4))unity negative feedback
ω = rad/s
6.Hard
R(s)+Kcontroller+D(s)+3s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 3/(s + 4) in a unity negative feedback loop. A disturbance step of size 5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.0375.

G(s) = 3/(s + 4)D = 5css ≤ 0.0375
K =

Answer key

  1. 1. css = 2.857
  2. 2. T = 46.67
  3. 3. τ = 0.01351 s
  4. 4. K = 9
  5. 5. ω = 2 rad/s
  6. 6. K = 132

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