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)+11s + 3G(s)C(s)−

A plant G(s) = 11/(s + 3) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 11/(s + 3)unity negative feedback
p =
2.Easy
R(s)+14GC(s)0.025H+

An amplifier with gain G = 14 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 = 14H = 0.025positive feedback
T =
3.Medium
R(s)+7(s + 4)(s + 3)(s + 6)G(s)C(s)−

A unity negative feedback loop has G(s) = 7(s + 4)/((s + 3)(s + 6)). A step of size 5 is applied at the reference. Find the steady-state error ess.

G(s) = 7(s + 4)/((s + 3)(s + 6))R = 5
ess =
4.Medium
R(s)+58s(s + 7)G(s)C(s)−

A unity negative feedback loop has G(s) = 58/(s(s + 7)). The reference is a ramp r(t) = 10·t. Find the steady-state error ess.

G(s) = 58/(s(s + 7))r(t) = 10·t
ess =
5.Hard
R(s)+64s(s + 4)G(s)C(s)1H−

The plant G(s) = 64/(s(s + 4)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 64/(s(s + 4))H = 1
σ =
6.Hard
R(s)+4s + 2G₁+3s + 1G₂C(s)0.5H₁−1H₂−

Reduce the block diagram with G₁ = 4/(s + 2), G₂ = 3/(s + 1), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 4/(s + 2)G₂ = 3/(s + 1)H₁ = 0.5H₂ = 1
T(0) =

Answer key

  1. 1. p = −14
  2. 2. T = 21.54
  3. 3. ess = 1.957
  4. 4. ess = 1.207
  5. 5. σ = −2
  6. 6. T(0) = 0.7059

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