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)+11GC(s)0.02H+

An amplifier with gain G = 11 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 11H = 0.02positive feedback
T =
2.Easy
R(s)+1s + 9G(s)C(s)−

A plant G(s) = 1/(s + 9) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 1/(s + 9)unity negative feedback
p =
3.Medium
R(s)+30s + 4G(s)C(s)0.25H−

A plant G(s) = 30/(s + 4) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. Find the time constant τ of the closed loop.

G(s) = 30/(s + 4)H = 0.25
τ = s
4.Medium
R(s)+13K+4s + 6G(s)C(s)3H₁−−

The plant G(s) = 4/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 3. A controller gain K = 13 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 4/(s + 6)H₁ = 3K = 13
p =
5.Hard
R(s)+K(s + 4)(s + 5)(s + 8)G(s)C(s)−

The plant G(s) = K/((s + 4)(s + 5)(s + 8)) is in a unity negative feedback loop. At the largest stable gain the loop oscillates. Find the frequency of oscillation ω in rad/s.

G(s) = K/((s + 4)(s + 5)(s + 8))unity negative feedback
ω = rad/s
6.Hard
R(s)+13s + 1G₁+1s + 4G₂C(s)4H₁−0.1H₂−

Reduce the block diagram with G₁ = 13/(s + 1), G₂ = 1/(s + 4), an inner negative feedback H₁ = 4 around G₂ and an outer negative feedback H₂ = 0.1. Find the DC gain T(0) of C(s)/R(s).

G₁ = 13/(s + 1)G₂ = 1/(s + 4)H₁ = 4H₂ = 0.1
T(0) =

Answer key

  1. 1. T = 14.1
  2. 2. p = −10
  3. 3. τ = 0.08696 s
  4. 4. p = −70
  5. 5. ω = 9.592 rad/s
  6. 6. T(0) = 1.398

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