ndnger wrote on May 10th, 2009, 11:37pm:I haven't used Nyquist criteria to prove stability and as you've stated that any analysis technique gives that the system is stable.
So my result is not contradicting any of these other analysis methods.
No. Your story is contradicting.
Again, if your story is correct, even a simple system which is judged as unstable by Nyquist Criteria will be stable.
ndnger wrote on May 10th, 2009, 11:37pm:Now my question to you is why should the red dot frequency create a RHP pole.
In other words, why should this loop have RHP, given that the loop gain has 360 deg phase shift,
Again see Nyquist Diagram of
http://www.designers-guide.org/Forum/YaBB.pl?num=1190272820/0#0In this situation, there is no pole for A/(1+A) in RHP.
However if yellow point moves on Real-Axis inside magenta unit circle or blue point moves on Real-Axis outside magenta unit circle in Nyquist Diagram, system will be unstable,
although red point remains in same point.
Here some poles for A/(1+A) in RHP will be created by this yellow point or blue point movement.
ndnger wrote on May 10th, 2009, 11:37pm:but remember we are looking at the input to output transfer function, ie, A/(1+A)?
This is your basic misunderstanding point about stability for system.In studying stability of system, an important factor which we have to focus on is
"Characteristics Polynomial" not "Input to Output Transfer Function".
http://en.wikipedia.org/wiki/Nyquist_stability_criterionAnd you have to learn "Internal Stability" which is more extended issue about Stability, here we can't argue it's stability by "Input to Output Transfer Function".
State Space Formulation is required
http://www.designers-guide.org/Forum/YaBB.pl?num=1241534678/4#4But your misunderstanding is not related to this "Internal Stability".
Your misunderstanding is more basic.
ndnger wrote on May 10th, 2009, 11:37pm:Also the michigan website link says that open loop transfer function becomes confusing when the open loop transfer function has poles on the jw axis.
But your open loop system doesn't have any pole on the jw axis,
so bode plot (and A/(1+A)) can be used to make judgements on stability.
I can't understand what you want to claim.
If open loop function is completely lossless, Nyquist Diagram is never closed in finite region of complex plane.
Maybe the michigan website explains this issue in Nyquist Diagram using MATLAB, although this is not problem at all.
I just wanted to show very simple Nyquist Diagram for unstable system which has only one crossing point in negative Real-Axis
to show
"If your story is correct, even a simple system which is judged as unstable by Nyquist Criteria will be stable".Maybe the michigan website is not good example for this purpose.
And this michigan website doesn't argue "Conditionally Stable System" at all.
The followings are more proper as example.
See page.11 of
http://www-control.eng.cam.ac.uk/gv/p6/Handout6.pdfSee page.3 of
http://www.staff.ncl.ac.uk/j.w.finch/CS_notes_2.pdfndnger wrote on May 10th, 2009, 11:37pm:BTW, I was referring to spectre, when I said cadence.
It is no more than common "SPICE" although Cadence call it as "Spectre".
If I have to choose one from many SPICE type simulators, I use HSPICE which is Golden Standard Simulator.
http://www.designers-guide.org/Forum/YaBB.pl?num=1238150066/5#5