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)+8G₁5G₂C(s)1H−

In the block diagram the forward path has the gains G₁ = 8 and G₂ = 5 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 8G₂ = 5H = 1
T =
2.Easy
R(s)+19GC(s)0.04H+

An amplifier with gain G = 19 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 = 19H = 0.04positive feedback
T =
3.Medium
R(s)+4(s + 5)(s + 4)(s + 7)G(s)C(s)−

A unity negative feedback loop has G(s) = 4(s + 5)/((s + 4)(s + 7)). A step of size 2 is applied at the reference. Find the steady-state error ess.

G(s) = 4(s + 5)/((s + 4)(s + 7))R = 2
ess =
4.Medium
R(s)+3(s + 6)(s + 2)(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 3(s + 6)/((s + 2)(s + 8)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 3(s + 6)/((s + 2)(s + 8))R = 5
ess =
5.Hard
R(s)+7s + 4G₁+3s + 3G₂C(s)1H₁−0.25H₂−

Reduce the block diagram with G₁ = 7/(s + 4), G₂ = 3/(s + 3), an inner negative feedback H₁ = 1 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 7/(s + 4)G₂ = 3/(s + 3)H₁ = 1H₂ = 0.25
T(0) =
6.Hard
R(s)+60s(s + 6)G(s)C(s)2H−

The plant G(s) = 60/(s(s + 6)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 60/(s(s + 6))H = 2
ωd = rad/s

Answer key

  1. 1. T = 0.9756
  2. 2. T = 79.17
  3. 3. ess = 1.167
  4. 4. ess = 2.353
  5. 5. T(0) = 0.7179
  6. 6. ωd = 10.54 rad/s

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