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)+8GC(s)0.04H+

An amplifier with gain G = 8 has positive feedback through a path with gain H = 0.04 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 8H = 0.04positive feedback
T =
2.Easy
R(s)10G₂5G₃+−4G₁C(s)

The signal R splits into two parallel blocks G₂ = 10 and G₃ = 5. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 4. Find the overall gain T = C/R.

G₁ = 4G₂ = 10G₃ = 5signs: + G₂, − G₃
T =
3.Medium
R(s)+22s + 9G(s)C(s)0.1H−

A plant G(s) = 22/(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) = 22/(s + 9)H = 0.1
τ = s
4.Medium
R(s)+5(s + 6)(s + 5)(s + 8)G(s)C(s)−

A unity negative feedback loop has G(s) = 5(s + 6)/((s + 5)(s + 8)). A step of size 1 is applied at the reference. Find the steady-state error ess.

G(s) = 5(s + 6)/((s + 5)(s + 8))R = 1
ess =
5.Hard
R(s)+K(s + 5)(s + 6)(s + 7)G(s)C(s)−

The plant G(s) = K/((s + 5)(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 + 5)(s + 6)(s + 7))unity negative feedback
Kmax =
6.Hard
R(s)+56s(s + 6)G(s)C(s)0.5H−

The plant G(s) = 56/(s(s + 6)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 56/(s(s + 6))H = 0.5
ωd = rad/s

Answer key

  1. 1. T = 11.76
  2. 2. T = 20
  3. 3. τ = 0.08929 s
  4. 4. ess = 0.5714
  5. 5. Kmax = 1716
  6. 6. ωd = 4.359 rad/s

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