How to find the intersection of Nyquist curve and real axis, that is, the specific point

Find w whose phase angle condition is equal to-180 degrees, and bring w into the modulus condition, and its value is the absolute value of the intersection point.

Let the phase angle be equal to 180 or 0, first find out oumiga, bring it into the original formula, and find out the amplitude.

The Nyquist curve corresponds to the relationship between w and G(jw), and the intersection of the curve and the imaginary axis can be solved by solving the phase angle ψ (W) = 90? ++2kπ gets the corresponding w and brings it into G(jw) to get the intersection with the imaginary axis. Similarly, the intersection with the real axis can solve the W when the phase angle equation is equal to-180 and bring it in.

Extended data:

Nyquist curve: For a continuous-time linear time-invariant system, the gain and phase of its frequency response are plotted in polar coordinates. Named after the American scientist Nyquist, who originated in Sweden, for his contribution to control theory. Each point on the graph corresponds to the frequency response at a specific frequency. The angle of the point relative to the origin indicates the phase, and the distance between the point and the origin indicates the gain. This curve can provide the information of transfer function and can be used to judge whether a system with feedback is stable or not.

Baidu Encyclopedia-Nyquist Curve