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)+18s + 8G(s)C(s)−

A plant G(s) = 18/(s + 8) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 18/(s + 8)unity negative feedback
p =
2.Easy
R(s)+13s + 3G(s)C(s)−

A plant G(s) = 13/(s + 3) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 13/(s + 3)unity negative feedback
p =
3.Medium
R(s)+25s + 9G(s)C(s)0.1H−

A plant G(s) = 25/(s + 9) is controlled in a negative feedback loop whose sensor has the gain H = 0.1. Find the time constant τ of the closed loop.

G(s) = 25/(s + 9)H = 0.1
τ = s
4.Medium
R(s)+48s(s + 2)G(s)C(s)−

A unity negative feedback loop has G(s) = 48/(s(s + 2)). The reference is a ramp r(t) = 5·t. Find the steady-state error ess.

G(s) = 48/(s(s + 2))r(t) = 5·t
ess =
5.Hard
R(s)+Ks(s + 6)(s + 7)G(s)C(s)−

The plant G(s) = K/(s(s + 6)(s + 7)) 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(s + 6)(s + 7))unity negative feedback
ω = rad/s
6.Hard
R(s)+32s(s + 4)G(s)C(s)2H−

The plant G(s) = 32/(s(s + 4)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 32/(s(s + 4))H = 2
σ =

Answer key

  1. 1. p = −26
  2. 2. p = −16
  3. 3. τ = 0.08696 s
  4. 4. ess = 0.2083
  5. 5. ω = 6.481 rad/s
  6. 6. σ = −2

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