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)8G₂8G₃++2G₁C(s)

The signal R splits into two parallel blocks G₂ = 8 and G₃ = 8. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 2. Find the overall gain T = C/R.

G₁ = 2G₂ = 8G₃ = 8signs: + G₂, + G₃
T =
2.Easy
R(s)+11GC(s)0.02H+

An amplifier with gain G = 11 has positive feedback through a path with gain H = 0.02 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 11H = 0.02positive feedback
T =
3.Medium
R(s)+5(s + 1)(s + 7)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 5(s + 1)/((s + 7)(s + 9)). A step of size 2 is applied at the reference. Find the steady-state error ess.

G(s) = 5(s + 1)/((s + 7)(s + 9))R = 2
ess =
4.Medium
R(s)+Ks(s + 6)G(s)C(s)−

The plant G(s) = K/(s(s + 6)) 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 + 6))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+5s + 2plantC(s)−

A proportional controller K drives the plant G(s) = 5/(s + 2) in a unity negative feedback loop. A disturbance step of size 10 enters at the plant input while R = 0. Find the smallest gain K that keeps the steady-state output at or below 0.25.

G(s) = 5/(s + 2)D = 10css ≤ 0.25
K =
6.Hard
R(s)+62s(s + 8)G(s)C(s)2H−

The plant G(s) = 62/(s(s + 8)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 62/(s(s + 8))H = 2
σ =

Answer key

  1. 1. T = 32
  2. 2. T = 14.1
  3. 3. ess = 1.853
  4. 4. K = 9
  5. 5. K = 39.6
  6. 6. σ = −4

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