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)+18s + 6G(s)C(s)−

A plant G(s) = 18/(s + 6) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 18/(s + 6)unity negative feedback
T(0) =
2.Easy
R(s)+18GC(s)0.025H+

An amplifier with gain G = 18 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 = 18H = 0.025positive feedback
T =
3.Medium
R(s)+2K+10s + 7G(s)C(s)3H₁−−

The plant G(s) = 10/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 3. A controller gain K = 2 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 10/(s + 7)H₁ = 3K = 2
T(0) =
4.Medium
R(s)+K(s + 7)(s + 9)G(s)C(s)−

The plant G(s) = K/((s + 7)(s + 9)) 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 + 7)(s + 9))unity negative feedback
K =
5.Hard
R(s)+16s(s + 3)G(s)C(s)2H−

The plant G(s) = 16/(s(s + 3)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 16/(s(s + 3))H = 2
σ =
6.Hard
R(s)+Kcontroller+D(s)+4s + 3plantC(s)−

A proportional controller K drives the plant G(s) = 4/(s + 3) in a unity negative feedback loop. A disturbance step of size 0.5 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.01333.

G(s) = 4/(s + 3)D = 0.5css ≤ 0.01333
K =

Answer key

  1. 1. T(0) = 0.75
  2. 2. T = 32.73
  3. 3. T(0) = 0.3509
  4. 4. K = 1
  5. 5. σ = −1.5
  6. 6. K = 36.75

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