Exercise 1.3

Exercise 1.3#

Analysis ∙ Linear dynamical systems

../_images/ex5.png

Fig. 5 Step responses to consider (courtesy of Exercise Manual for Automatic Control)#

Pair each step response in the plot above with the correct transfer function from the list below:

  1. \(G_1(s) = \frac{2}{s^2 + s + 1}\)

  2. \(G_2(s) = \frac{1}{s^2 + s + 1}\)

  3. \(G_3(s) = \frac{1}{s^2 + 0.1s + 1}\)

  4. \(G_4(s) = \frac{1}{s^2 + 2s + 1}\)

Useful formulas to compute the damping ratio and natural frequency of complex-conjugate eigevalues are reported in the Useful formulas.