How do I assign the following Bode plots to their corresponding Nyquist diagram?Can i tell the number of poles of the transfer function of the nyquist plot, by looking at w→infinity (from which of the four axis directions G(s) goes into the origin)?
I would have guessed, that:
- (1) is of the form \$ G(s) = -\frac{1}{(s+a)}\$ with \$ a>0 \$
- (2) is of the form \$ G(s) = \frac{1}{(s+a)}\$ with \$ a>0 \$
- (3) is of the form \$ G(s) = \frac{1}{(s+a)(s+b)}\$ with \$ a,b>0 \$
- (4) is of the form \$ G(s) = \frac{1}{(s)}\$ plus some other poles i dont know
- (a) is of the form \$ G(s) = \frac{1}{\frac{s}{2}+1} \$ or \$ \frac{2}{s+2} \$
- (b) is of the form \$ G(s) = \frac{1}{s(2s+1)} \$ or \$ \frac{0.5}{s(s+0.5)} \$
- (c) is of the form \$ G(s) = \frac{s}{\frac{s}{2}+1} \$ or \$ \frac{2s}{s+2} \$
- (d) is of the form \$ G(s) = \frac{1}{(s+1)(\frac{s}{10}+1)} \$ or \$ \frac{10}{(s+1)(s+10)} \$
while (b) and (d) are missing the gain constant and thus (d) for example is stretched from 0 to 2 instead of 0 to 1. But thats not an issue, when all we want is assigning the bode and nyquist plots, right?
Also im bugged by (1) and (2) being identical (?)I dont know how to put it in words but as theres only one half of the nyquist plot "circle" i assume we only go from 0 to infinity for the plot?So a flip among the real axis indicates a minus in the gain constant, right?
If so, i can assume (c) has a negative gain constant, right?
My guess:
- (a) and (2)
- (b) and (4)
- (c) and (1) //c (bode) has a zero in the origin but 1 (nyquist) doesnt - what did i do wrong here? I guess the mistake is on the "nyquist side" analysis
- (d) and (3)
