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)+6G₁10G₂C(s)0.2H−

In the block diagram the forward path has the gains G₁ = 6 and G₂ = 10 in series, and the negative feedback path has the gain H = 0.2. Find the overall gain T = C/R.

G₁ = 6G₂ = 10H = 0.2
T =
2.Easy
R(s)+7GC(s)0.1H+

An amplifier with gain G = 7 has positive feedback through a path with gain H = 0.1 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 7H = 0.1positive feedback
T =
3.Medium
R(s)+Ks(s + 5)G(s)C(s)−

The plant G(s) = K/(s(s + 5)) 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(s + 5))unity negative feedback
K =
4.Medium
R(s)+11K+3s + 7G(s)C(s)1H₁−−

The plant G(s) = 3/(s + 7) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 11 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 3/(s + 7)H₁ = 1K = 11
p =
5.Hard
R(s)+Kcontroller+D(s)+1s + 10plantC(s)−

A proportional controller K drives the plant G(s) = 1/(s + 10) in a unity negative feedback loop. A disturbance step of size 10 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.2.

G(s) = 1/(s + 10)D = 10css ≤ 0.2
K =
6.Hard
R(s)+48s(s + 6)G(s)C(s)1H−

The plant G(s) = 48/(s(s + 6)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 48/(s(s + 6))H = 1
σ =

Answer key

  1. 1. T = 4.615
  2. 2. T = 23.33
  3. 3. K = 6.25
  4. 4. p = −43
  5. 5. K = 40
  6. 6. σ = −3

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