A control system has the following open-loop transfer function: Ls= 2 s2 +0.6s +9 /3 s2 1
a) Draw the Bode magnitude and the phase plots for L(s). Use two plots to draw the contribution of each factor (i. e., constant gain, zeros, poles) and other two for the magnitude and phase of L(s)
In particular:
Draw the asymptotes and indicate their slopes, then sketch the real curves.
Clearly mark the cutoff frequencies.
b) Calculate the phase margin (PM), the crossover frequency (Wc) and indicate them on the Bode plots. Using φΡΜ, estimate the damping ratio ζ for the closed-loop poles
c) Calculate the gain margin GM, the frequency at -180 deg (w- π) and indicate them on the Bode plots.
d) Calculate the bandwidth (WB) and the gain in dB for w -[infinity] and indicate them on the Bode plots.
e) Calculate the resonance frequency (wr) and the magnitude at such frequency (i. e. 20LogL(iw)) and indicate the values on the Bode plots For parts b) through e), indicate all the quantities in the second pair of plots .