Hi everyone, i'm real confused and stucked about a point in applying Nyquist stability criterion... now i'll explain why.(adsbygoogle = window.adsbygoogle || []).push({});

I know that it's needed to know how many times i'm wrapping the nyquist critical point (-1;0) with my plot, and i'm enough good to draw by hand a nyquist plot, but the problem is to determine analitically the intersection value of the plot in which i'm interssecting the real axes, i've heard that i have to substitute 'jω' in my transfer function and after i have to divide the real part from the imaginary part of my transfer function and then find out the ω where I'm intersecting the real axes putting the real part of the transfer function equal to zero. Mathematically speaking : RealPart(F(jω))=0 where F is my transfer function.

Once i've found the ω i substitute that ω in my transfer function to find the exact point where i'm intersecting the real axes.

My first question is : Is there a quicker way to compute this point without using software, since I need it for a test ?

I've heard about the arctan way of computing the phase, but the problem is that if I put an equation (for example) like this :

arctan(w/3)+arctan(w/5)-3arctan(w/10)=-180

it's impossible for me to solve it...i don't know how to handle these arctan equations, my second question is : Is there a way to compute it ? And if not, which is the way to solve this problem ?

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# Nyquist Plot Intersection with Real Axes

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