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)+18G₁5G₂C(s)1H−

In the block diagram the forward path has the gains G₁ = 18 and G₂ = 5 in series, and the negative feedback path has the gain H = 1. Find the overall gain T = C/R.

G₁ = 18G₂ = 5H = 1
T =
2.Easy
R(s)+6G₁9G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 6 and G₂ = 9 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 6G₂ = 9H = 0.05
T =
3.Medium
R(s)+20K+2s + 6G(s)C(s)2H₁−−

The plant G(s) = 2/(s + 6) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 20 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 2/(s + 6)H₁ = 2K = 20
p =
4.Medium
R(s)+24s(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 24/(s(s + 9)). The reference is a ramp r(t) = 5·t. Find the steady-state error ess.

G(s) = 24/(s(s + 9))r(t) = 5·t
ess =
5.Hard
R(s)+K(s + 1)(s + 6)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 1)(s + 6)(s + 7)) 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 + 1)(s + 6)(s + 7))unity negative feedback
Kmax =
6.Hard
R(s)+Ks(s + 1)(s + 6)G(s)C(s)−

The plant G(s) = K/(s(s + 1)(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(s + 1)(s + 6))unity negative feedback
Kmax =

Answer key

  1. 1. T = 0.989
  2. 2. T = 14.59
  3. 3. p = −50
  4. 4. ess = 1.875
  5. 5. Kmax = 728
  6. 6. Kmax = 42

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