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)9G₂1G₃+−5G₁C(s)

The signal R splits into two parallel blocks G₂ = 9 and G₃ = 1. Their outputs meet at a summing junction with the signs shown (+ and −), and the sum passes through G₁ = 5. Find the overall gain T = C/R.

G₁ = 5G₂ = 9G₃ = 1signs: + G₂, − G₃
T =
2.Easy
R(s)+2s + 3G(s)C(s)−

A plant G(s) = 2/(s + 3) is placed in a unity negative feedback loop. Find the closed-loop pole p.

G(s) = 2/(s + 3)unity negative feedback
p =
3.Medium
R(s)+3(s + 6)(s + 7)(s + 9)G(s)C(s)−

A unity negative feedback loop has G(s) = 3(s + 6)/((s + 7)(s + 9)). A step of size 1 is applied at the reference. Find the steady-state error ess.

G(s) = 3(s + 6)/((s + 7)(s + 9))R = 1
ess =
4.Medium
R(s)+Ks(s + 13)G(s)C(s)−

The plant G(s) = K/(s(s + 13)) 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 + 13))unity negative feedback
K =
5.Hard
R(s)+76s(s + 5)G(s)C(s)2H−

The plant G(s) = 76/(s(s + 5)) 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) = 76/(s(s + 5))H = 2
ωd = rad/s
6.Hard
R(s)+24controller+D(s)+3s + 3plantC(s)−

A proportional controller K = 24 drives the plant G(s) = 3/(s + 3) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). With R = 0, a disturbance step of size 2 is applied. Find the steady-state output css.

K = 24G(s) = 3/(s + 3)D = 2R = 0
css =

Answer key

  1. 1. T = 40
  2. 2. p = −5
  3. 3. ess = 0.7778
  4. 4. K = 42.25
  5. 5. ωd = 12.07 rad/s
  6. 6. css = 0.08

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