{"id":7539,"date":"2022-04-01T13:23:14","date_gmt":"2022-04-01T07:53:14","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7539"},"modified":"2022-04-08T21:33:18","modified_gmt":"2022-04-08T16:03:18","slug":"what-is-the-nyquist-stability-criterion","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-the-nyquist-stability-criterion\/","title":{"rendered":"What is the Nyquist Stability Criterion?"},"content":{"rendered":"\n

Nyquist Stability Criterion gives the frequency response as well as comments on the stability<\/a> and the relative stability of the system.<\/p>\n\n\n\n

Nyquist Stability Criteria:<\/h2>\n\n\n\n

The semi graphical method which we use to determine the stability of a closed loop system by investigating the properties of the frequency domain plot (Polar plot). The Nyquist plot of the open loop transfer function G(S) H(S) is L(S)<\/p>\n\n\n\n

L(S) = G(S)H(S)<\/p>\n\n\n\n

The Nyquist plot of L(S) is a plot drawn by substituting S=jw and varying the value of w as per the polar plot. We plot the polar plot ranging 0 to – \u221e. But in the Nyquist plot the range of frequency is varied from ( -\u221e to 0 ) and (0 to \u221e ). Therefore, the Nyquist plot gives us the plot for the entire frequency range.<\/p>\n\n\n\n

Inferences from Nyquist Criteria<\/strong> :-<\/p>\n\n\n\n

(1). The Nyquist criterion mainly provides information on relative stability of a stable system and also the instability of any unstable system. It also provides information about the absolute stability of  the system. <\/p>\n\n\n\n

(2). It also provides information about the improvement of system stability. <\/p>\n\n\n\n

(3). As we know, the Nyquist plot of G(S) H(S) is the polar plot of G(S) H(S) with a wider range of frequency ( -\u221e to \u221e ) and along the Nyquist path.<\/p>\n\n\n\n

(4). The additional information like bandwidth, gain margin and phase margin is also provided by Nyquist plot. <\/p>\n\n\n\n

Construction of Nyquist Plot<\/h2>\n\n\n\n

Encircled<\/strong> : <\/h3>\n\n\n\n

A point or region in a complex function phase i.e. The S-plane is said to be encircled by a closed path if it is found inside the path.<\/p>\n\n\n\n

Assumptions :<\/p>\n\n\n\n

<\/p>\n\n\n\n

<\/p>\n\n\n\n

Let us consider the above figure where point A is encircled by the closed path Y. The point B being outside the closed path is not encircled by path Y. The encirclement made by the closed path Y are in either clockwise or in an anticlockwise direction.<\/p>\n\n\n\n

In figure b where again point A is encircled by Y in an anticlockwise direction. Therefore we can conclude that the region which lies inside the path is encircled and the outside path is not encircled.  <\/p>\n\n\n\n

Enclosed<\/strong> :-<\/h3>\n\n\n\n

A point or region is said to be enclosed by a closed path if it is encircled in the counterclockwise direction. In other cases a point or a region is said to be enclosed when it always lies to the left of the path, when the path has a definite direction.<\/p>\n\n\n\n

In the figure considered below the shaded area is said to be enclosed by a closed path Y. From the figure it is very clear that point A is enclosed by Y in fig a. but is not enclosed by Y in fig b. and for point B it is vice versa.<\/p>\n\n\n\n

<\/p>\n\n\n\n

<\/p>\n\n\n\n

No. of encirclements and enclosures : For A line is cut once as it\u2019s overlapping but two times in same direction<\/p>\n\n\n\n

<\/p>\n\n\n\n

When a point is encircled by a closed path Y, a no. N can be assigned to the no. of times it is encircled. By drawing an arrow around closed path Y we can determine the magnitude of N.<\/p>\n\n\n\n

Taking an arbitrary point S, and moving around in clockwise direction and anti-clockwise direction respectively. We are getting a direction.<\/p>\n\n\n\n

The direction is determined by the path followed by S1<\/sub>. The total number of revolutions by S1<\/sub> is N. This is only the net angle \u2018 2 \u03c0 N \u2019.<\/p>\n\n\n\n

For N = 2 = B   for A = 1 = N<\/p>\n\n\n\n

Now, point A is encircled (or 2 \u03c0 radians) by Y and point B is encircled twice (or 4 \u03c0 radians). Both are in clockwise direction.<\/p>\n\n\n\n

 In diagram B again A and B are encircled but in counter clockwise direction. Thus for this diagram A is enclosed and B is enclosed twice.<\/p>\n\n\n\n

By definition M is positive for anticlockwise(direction) encirclement and negative for clockwise encirclement.<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Nyquist Stability Criterion gives the frequency response as well as comments on the stability and the relative stability of the system.<\/p>\n","protected":false},"author":28,"featured_media":7542,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[37],"tags":[],"class_list":["post-7539","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electronics"],"yoast_head":"\nWhat is the Nyquist Stability Criterion? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"Nyquist Stability Criterion gives the frequency response as well as comments on the stability and the relative stability of the system.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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