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)+15s + 10G(s)C(s)−

A plant G(s) = 15/(s + 10) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 15/(s + 10)unity negative feedback
τ = s
2.Easy
R(s)+13G₁7G₂C(s)0.2H−

In the block diagram the forward path has the gains G₁ = 13 and G₂ = 7 in series, and the negative feedback path has the gain H = 0.2. Find the overall gain T = C/R.

G₁ = 13G₂ = 7H = 0.2
T =
3.Medium
R(s)+17K+3s + 2G(s)C(s)2H₁−−

The plant G(s) = 3/(s + 2) has an inner (minor) negative feedback loop with gain H₁ = 2. A controller gain K = 17 and an outer unity negative feedback loop close the system. Find the closed-loop pole p.

G(s) = 3/(s + 2)H₁ = 2K = 17
p =
4.Medium
R(s)+16s + 5G(s)C(s)0.1H−

A plant G(s) = 16/(s + 5) 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) = 16/(s + 5)H = 0.1
τ = s
5.Hard
R(s)+Kcontroller+D(s)+10s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 10/(s + 4) in a unity negative feedback loop. A disturbance step of size 1 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.05.

G(s) = 10/(s + 4)D = 1css ≤ 0.05
K =
6.Hard
R(s)+K(s + 2)(s + 4)(s + 5)G(s)C(s)−

The plant G(s) = K/((s + 2)(s + 4)(s + 5)) 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 + 2)(s + 4)(s + 5))unity negative feedback
Kmax =

Answer key

  1. 1. τ = 0.04 s
  2. 2. T = 4.74
  3. 3. p = −59
  4. 4. τ = 0.1515 s
  5. 5. K = 19.6
  6. 6. Kmax = 378

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