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)+11G₁2G₂C(s)0.1H−

In the block diagram the forward path has the gains G₁ = 11 and G₂ = 2 in series, and the negative feedback path has the gain H = 0.1. Find the overall gain T = C/R.

G₁ = 11G₂ = 2H = 0.1
T =
2.Easy
R(s)+17s + 7G(s)C(s)−

A plant G(s) = 17/(s + 7) is placed in a unity negative feedback loop. Find the time constant τ of the closed loop.

G(s) = 17/(s + 7)unity negative feedback
τ = s
3.Medium
R(s)+6s + 8G(s)C(s)0.25H−

A plant G(s) = 6/(s + 8) is controlled in a negative feedback loop whose sensor has the gain H = 0.25. A step of size 1 is applied at R. Find the steady-state output css.

G(s) = 6/(s + 8)H = 0.25R = 1
css =
4.Medium
R(s)+K(s + 4)(s + 12)G(s)C(s)−

The plant G(s) = K/((s + 4)(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 + 4)(s + 12))unity negative feedback
K =
5.Hard
R(s)+Kcontroller+D(s)+8s + 3plantC(s)−

A proportional controller K drives the plant G(s) = 8/(s + 3) 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 5.333.

G(s) = 8/(s + 3)D = 10css ≤ 5.333
K =
6.Hard
R(s)+22s(s + 11)G(s)C(s)2H−

The plant G(s) = 22/(s(s + 11)) is in a negative feedback loop with sensor gain H = 2. The closed-loop poles are complex. Find their real part σ.

G(s) = 22/(s(s + 11))H = 2
σ =

Answer key

  1. 1. T = 6.875
  2. 2. τ = 0.04167 s
  3. 3. css = 0.6316
  4. 4. K = 16
  5. 5. K = 1.5
  6. 6. σ = −5.5

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