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)+16GC(s)0.04H+

An amplifier with gain G = 16 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 = 16H = 0.04positive feedback
T =
2.Easy
R(s)+7G₁7G₂C(s)0.05H−

In the block diagram the forward path has the gains G₁ = 7 and G₂ = 7 in series, and the negative feedback path has the gain H = 0.05. Find the overall gain T = C/R.

G₁ = 7G₂ = 7H = 0.05
T =
3.Medium
R(s)+11(s + 3)(s + 2)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 11(s + 3)/((s + 2)(s + 9)). A step of size 2 is applied at the reference. Find the steady-state error ess.

G(s) = 11(s + 3)/((s + 2)(s + 9))R = 2
ess =
4.Medium
R(s)+Ks(s + 12)G(s)C(s)−

The plant G(s) = K/(s(s + 12)) 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 + 12))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+3s + 4plantC(s)−

A proportional controller K drives the plant G(s) = 3/(s + 4) in a unity negative feedback loop. A disturbance step of size 2 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.3.

G(s) = 3/(s + 4)D = 2css ≤ 0.3
K =
6.Hard
R(s)+62s(s + 3)G(s)C(s)2H−

The plant G(s) = 62/(s(s + 3)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 62/(s(s + 3))H = 2
ωd = rad/s

Answer key

  1. 1. T = 44.44
  2. 2. T = 14.2
  3. 3. ess = 0.7059
  4. 4. K = 36
  5. 5. K = 5.333
  6. 6. ωd = 11.03 rad/s

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