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)+16G₁5G₂C(s)0.25H−

In the block diagram the forward path has the gains G₁ = 16 and G₂ = 5 in series, and the negative feedback path has the gain H = 0.25. Find the overall gain T = C/R.

G₁ = 16G₂ = 5H = 0.25
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)+18K+3s + 2G(s)C(s)1H₁−−

The plant G(s) = 3/(s + 2) has an inner (minor) negative feedback loop with gain H₁ = 1. A controller gain K = 18 and an outer unity negative feedback loop close the system. Find the closed-loop DC gain T(0).

G(s) = 3/(s + 2)H₁ = 1K = 18
T(0) =
4.Medium
R(s)+K(s + 4)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 4)(s + 12)) 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 + 4)(s + 12))unity negative feedback
K =
5.Hard
R(s)+18s + 5G₁+5s + 8G₂C(s)2H₁−0.25H₂−

Reduce the block diagram with G₁ = 18/(s + 5), G₂ = 5/(s + 8), an inner negative feedback H₁ = 2 around G₂ and an outer negative feedback H₂ = 0.25. Find the DC gain T(0) of C(s)/R(s).

G₁ = 18/(s + 5)G₂ = 5/(s + 8)H₁ = 2H₂ = 0.25
T(0) =
6.Hard
R(s)+K(s + 3)(s + 4)(s + 6)G(s)C(s)−

The plant G(s) = K/((s + 3)(s + 4)(s + 6)) is in a unity negative feedback loop. Use the Routh–Hurwitz criterion to find the largest gain Kmax for which the closed loop is stable.

G(s) = K/((s + 3)(s + 4)(s + 6))unity negative feedback
Kmax =

Answer key

  1. 1. T = 3.81
  2. 2. T = 23.33
  3. 3. T(0) = 0.9153
  4. 4. K = 16
  5. 5. T(0) = 0.8
  6. 6. Kmax = 630

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