Question 1 The transfer function ๐บ ๐ +1 has a complex variable ๐ = ๐ + ๐๐. ๐ +โ3 a) Find |๐บ(๐ )| and โ (๐บ(๐ )), when the complex variable is at coordinates (i) (๐, ๐) = (0,1) (ii) (๐, ๐) = (0,100) (iii) (๐, ๐) = (0,0.1) (3 Points) b) Sketch the Bode plot of the frequency response ๐บ(๐๐) (3 Points)
Question 2 Consider the open-loop transfer function ๐พ๐บ(๐ ) = 3 ๐พ2 ๐ +6๐ +5๐ a) When K = 10, the bode plot is given by Figure 1. Indicate the frequency values on the diagram where there are changes in the magnitude slope. (2 Points) Given the Gain Margin (GM)=+8 dB, Phase Margin (PM)=+21o, on the bode plot on Figure 2, label (i) GM and (ii) PM. (2 Points) b) Suppose we look at K=100. (i) Sketch the Bode diagram (4 Points) (ii) Write down the new GM (2 Points) (iii) Show graphically on your sketch, how you would measure the new PM. (2 Points)
