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)0.04H+

An amplifier with gain G = 16 has positive feedback through a path with gain H = 0.04 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 16H = 0.04positive feedback
T =
2.Easy
R(s)+10G₁5G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 10 and G₂ = 5 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 10G₂ = 5H = 0.1
T =
3.Medium
R(s)+8s + 2G(s)C(s)0.2H−

A plant G(s) = 8/(s + 2) 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) = 8/(s + 2)H = 0.2
τ = s
4.Medium
R(s)+6s + 7G(s)C(s)0.5H−

A plant G(s) = 6/(s + 7) is controlled in a negative feedback loop whose sensor has the gain H = 0.5. A step of size 24 is applied at R. Find the steady-state output css.

G(s) = 6/(s + 7)H = 0.5R = 24
css =
5.Hard
R(s)+42s(s + 7)G(s)C(s)0.5H−

The plant G(s) = 42/(s(s + 7)) 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) = 42/(s(s + 7))H = 0.5
σ =
6.Hard
R(s)+64s(s + 9)G(s)C(s)0.5H−

The plant G(s) = 64/(s(s + 9)) 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 + 9))H = 0.5
σ =

Answer key

  1. 1. T = 44.44
  2. 2. T = 8.333
  3. 3. τ = 0.2778 s
  4. 4. css = 14.4
  5. 5. σ = −3.5
  6. 6. σ = −4.5

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