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)+16G₁2G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 16 and G₂ = 2 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 16G₂ = 2H = 0.05
T =
2.Easy
R(s)+11s + 8G(s)C(s)−

A plant G(s) = 11/(s + 8) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 11/(s + 8)unity negative feedback
τ = s
3.Medium
R(s)+Ks(s + 19)G(s)C(s)−

The plant G(s) = K/(s(s + 19)) 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(s + 19))unity negative feedback
K =
4.Medium
R(s)+3K+3s + 8G(s)C(s)4H₁−−

The plant G(s) = 3/(s + 8) has an inner (minor) negative feedback loop with gain H₁ = 4. A controller gain K = 3 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 3/(s + 8)H₁ = 4K = 3
p =
5.Hard
R(s)+4s + 4G₁+2s + 6G₂C(s)0.5H₁−0.2H₂−

Reduce the block diagram with G₁ = 4/(s + 4), G₂ = 2/(s + 6), an inner negative feedback H₁ = 0.5 around G₂ and an outer negative feedback H₂ = 0.2. Find the DC gain T(0) of C(s)/R(s).

G₁ = 4/(s + 4)G₂ = 2/(s + 6)H₁ = 0.5H₂ = 0.2
T(0) =
6.Hard
R(s)+24s(s + 3)G(s)C(s)2H−

The plant G(s) = 24/(s(s + 3)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 24/(s(s + 3))H = 2
σ =

Answer key

  1. 1. T = 12.31
  2. 2. τ = 0.05263 s
  3. 3. K = 90.25
  4. 4. p = −29
  5. 5. T(0) = 0.2703
  6. 6. σ = −1.5

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