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)+18s + 2G(s)C(s)−

A plant G(s) = 18/(s + 2) is placed in a unity negative feedback loop. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 18/(s + 2)unity negative feedbackR = 1
css =
2.Easy
R(s)2G₂5G₃++6G₁C(s)

The signal R splits into two parallel blocks G₂ = 2 and G₃ = 5. Their outputs meet at a summing junction with the signs shown (+ and +), and the sum passes through G₁ = 6. Find the overall gain T = C/R.

G₁ = 6G₂ = 2G₃ = 5signs: + G₂, + G₃
T =
3.Medium
R(s)+Ks(s + 14)G(s)C(s)−

The plant G(s) = K/(s(s + 14)) 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 + 14))unity negative feedback
K =
4.Medium
R(s)+3s + 5G(s)C(s)0.1H−

A plant G(s) = 3/(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) = 3/(s + 5)H = 0.1
τ = s
5.Hard
R(s)+62s(s + 2)G(s)C(s)1H−

The plant G(s) = 62/(s(s + 2)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their imaginary part ωd (the positive value), in rad/s.

G(s) = 62/(s(s + 2))H = 1
ωd = rad/s
6.Hard
R(s)+9controller+D(s)+5s + 9plantC(s)−

A proportional controller K = 9 drives the plant G(s) = 5/(s + 9) in a unity negative feedback loop. A disturbance D enters at the plant input (it is added to the controller output). A reference step of size 1 and a disturbance step of size 5 are applied together. Find the steady-state output css.

K = 9G(s) = 5/(s + 9)D = 5R = 1
css =

Answer key

  1. 1. css = 0.9
  2. 2. T = 42
  3. 3. K = 49
  4. 4. τ = 0.1887 s
  5. 5. ωd = 7.81 rad/s
  6. 6. css = 1.296

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