Question

4. Consider the Bode Plots for G(s) (a) In a frequency region where the Bode phase curve is decreasing, which direction is the corresponding Nyquist curve moving ? Clockwise or counterclockwise? (b) Assume that the Bode plots for G(jw)| and the phase ф(w) are correct. Give the corresponding complex value on the Nyquist plot in terms of G(jw) and ф(W) (c) On the Bode plots for GGW)| and ф(W). how much must ф(w) change for there to be three encirclements of a region on the real axis , for the Nyquist plot? (d) Clearly, accurate Bode plots enable us to construct Nvauist plots, Can we accurately construct Bode plots from the Nyquist plot? Why?

Answer 1

(a) Since phase or angle curve is decreasing, therefore, the nyquist curve must be moving in the clock-wise direction.

(b) This problem is very simple ==>

Polar coordinates of the points in the nyquist or plot = $(\left | G(j\omega ) \right |, \phi (\omega ))$

Therefore, corresponding complex value = $\left | G(j\omega ) \right |e^{j\phi (\omega )}$ = $\left | G(j\omega ) \right |cos{(\phi (\omega ))} + j*\left | G(j\omega ) \right |sin{(\phi (\omega ))}$ ==> ANSWER

(c) Since, one encirclement = 360 degrees

Therefore, 3 encirclements = 960 degrees ==> ANSWER

(d) No, it is because we don't know the frequency values corresponding to points in the nyquist plot.

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