Conditional stability, I like to think about it this way: <\/p>\n
The ultimate test of stability is knowing whether the poles of the closed loop system are in the LHP. If so, it is stable. <\/p>\n
We get at the poles of the system by looking at the characteristic equation, 1+T(s). Unfortunately, we don’t have the math available (except in classroom exercises) we have an empirical system that may or may not be reduced to a mathematical model. For power supplies, even if they can be reduced to a model, it is approximate and just about always has significant deviations from the hardware. That is why measurements persist in this industry. <\/p>\n
Nyquist came up with a criterion for making sure that the poles are in the LHP by drawing his diagram. When you plot the vector diagram of T(s) is must not encircle the -1 point. <\/p>\n
Bode realized that the Nyquist diagram was not good for high gain since it plotted a linear scale of the magnitude, so he came up with his Bode plot which is what everyone uses. The Bode criteria only says that the phase must be above -180 degrees when it crosses over 0 dB. There is nothing that says it can’t do that before 0 dB. <\/p>\n
If you draw the Nyquist diagram of a conditionally stable system, you’ll see it doesn’t surround the -1 point. <\/p>\n
If you like, I can put some figures together. Or maybe a video would be a good topic. <\/p>\n
All this is great of course, but it’s still puzzling to think of how a sine wave can chase itself around the loop, get amplified and inverted, phase shifted another 180 degrees, and not be unstable! <\/p>\n
Having said all this about Nyquist, it is not something I plot in the lab. I just use it as an educational tool. In the lab, in courses, or consulting for clients, the Bode plot of gain and phase is what we use.<\/p>\n","protected":false},"excerpt":{"rendered":"
Conditional stability, I like to think about it this way: <\/p>\n
The ultimate test of stability is knowing whether the poles of the closed loop system are in the LHP. If so, it is stable. <\/p>\n
We get at the poles of the system by looking at the characteristic equation, 1+T(s). Unfortunately, we don’t have the math available (except in classroom exercises) we have an empirical system that may or may not be reduced to a mathematical model. For power supplies, even if they can be reduced to a model, it is approximate and just about always has significant deviations from the hardware. That is why measurements persist in this industry. <\/p>\n
Nyquist came up with a criterion for making sure that the poles are in the LHP by drawing his diagram. When you plot the vector diagram of T(s) is must not encircle the -1 point. <\/p>\n
Bode realized that the Nyquist diagram was not good for high gain since it plotted a linear scale of the magnitude, so he came up with his Bode plot which is what everyone uses. The Bode criteria only says that the phase must be above -180 degrees when it crosses over 0 dB. There is nothing that says it can’t do that before 0 dB. <\/p>\n
If you draw the Nyquist diagram of a conditionally stable system, you’ll see it doesn’t surround the -1 point. <\/p>\n
If you like, I can put some figures together. Or maybe a video would be a good topic. <\/p>\n
All this is great of course, but it’s still puzzling to think of how a sine wave can chase itself around the loop, get amplified and inverted, phase shifted another 180 degrees, and not be unstable! <\/p>\n
Having said all this about Nyquist, it is not something I plot in the lab. I just use it as an educational tool. In the lab, in courses, or consulting for clients, the Bode plot of gain and phase is what we use.<\/p>\n","protected":false},"author":0,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[67],"tags":[],"class_list":["post-14033","post","type-post","status-publish","format-standard","hentry","category-iacdrive_blog"],"_links":{"self":[{"href":"http:\/\/iacdrive.com\/index.php?rest_route=\/wp\/v2\/posts\/14033","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/iacdrive.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/iacdrive.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"http:\/\/iacdrive.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14033"}],"version-history":[{"count":0,"href":"http:\/\/iacdrive.com\/index.php?rest_route=\/wp\/v2\/posts\/14033\/revisions"}],"wp:attachment":[{"href":"http:\/\/iacdrive.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14033"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/iacdrive.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14033"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/iacdrive.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}