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)+10G₁5G₂C(s)0.5H−

In the block diagram the forward path has the gains G₁ = 10 and G₂ = 5 in series, and the negative feedback path has the gain H = 0.5. Find the overall gain T = C/R.

G₁ = 10G₂ = 5H = 0.5
T =
2.Easy
R(s)+12GC(s)0.04H+

An amplifier with gain G = 12 has positive feedback through a path with gain H = 0.04 (the feedback signal is added at the summing junction). Find the closed-loop gain T = C/R.

G = 12H = 0.04positive feedback
T =
3.Medium
R(s)+48s(s + 1)G(s)C(s)−

A unity negative feedback loop has G(s) = 48/(s(s + 1)). The reference is a ramp r(t) = 1·t. Find the steady-state error ess.

G(s) = 48/(s(s + 1))r(t) = 1·t
ess =
4.Medium
R(s)+Ks(s + 17)G(s)C(s)−

The plant G(s) = K/(s(s + 17)) 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 + 17))unity negative feedback
K =
5.Hard
R(s)+50s(s + 11)G(s)C(s)1H−

The plant G(s) = 50/(s(s + 11)) is in a negative feedback loop with sensor gain H = 1. The closed-loop poles are complex. Find their real part σ.

G(s) = 50/(s(s + 11))H = 1
σ =
6.Hard
R(s)+26s(s + 4)G(s)C(s)0.5H−

The plant G(s) = 26/(s(s + 4)) is in a negative feedback loop with sensor gain H = 0.5. The closed-loop poles are complex. Find their real part σ.

G(s) = 26/(s(s + 4))H = 0.5
σ =

Answer key

  1. 1. T = 1.923
  2. 2. T = 23.08
  3. 3. ess = 0.02083
  4. 4. K = 72.25
  5. 5. σ = −5.5
  6. 6. σ = −2

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