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)+4G₁4G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 4 and G₂ = 4 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 4G₂ = 4H = 0.1
T =
2.Easy
R(s)+20s + 1G(s)C(s)−

A plant G(s) = 20/(s + 1) is placed in a unity negative feedback loop. Find the closed-loop DC gain T(0).

G(s) = 20/(s + 1)unity negative feedback
T(0) =
3.Medium
R(s)+40s + 1G(s)C(s)0.1H−

A plant G(s) = 40/(s + 1) 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) = 40/(s + 1)H = 0.1
τ = s
4.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 =
5.Hard
R(s)+76s(s + 11)G(s)C(s)2H−

The plant G(s) = 76/(s(s + 11)) 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 + 11))H = 2
ωd = rad/s
6.Hard
R(s)+11controller+D(s)+3s + 6plantC(s)−

A proportional controller K = 11 drives the plant G(s) = 3/(s + 6) 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 10 is applied. Find the steady-state output css.

K = 11G(s) = 3/(s + 6)D = 10R = 0
css =

Answer key

  1. 1. T = 6.154
  2. 2. T(0) = 0.9524
  3. 3. τ = 0.2 s
  4. 4. K = 49
  5. 5. ωd = 11.03 rad/s
  6. 6. css = 0.7692

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