raja.cedt wrote on Oct 6th, 2009, 3:44am:hi buddypoor, i saw many times this stability discussions in many places..but no one concluded. Why don't you summaries. I am giving my conclusions here.
Bode plot will give decent results in the following cases
1.Both mag and phase plot should be monotonic
2. all pole system or system with one zero
Please correct the following and add your's also
thanks,
rajasekhar.
Hi rajasekhar,
a final conclusion (i. e. a summary of stability criteria) cannot be done in short. I think, here in the forum we should not and cannot repeat the contents of a textbook. For my opinion, it is not so easy as you have written in your conclusion.
For example: What do you mean with "Bode plot gives results". Do you refer to the slope of the magnitude and/or the phase information ?
If yes, you only speak of the simplified Nyquist criterion which applies only under some restrictions.
However, the BODE plot can be used for a stability check also in case of poles and zeros in the RHP (instability of the open loop).
But in this case the Nyquist criterion may NOT be transferred to BODE in its simplified form. Instead, you have to count the crossings of the 180 deg-line with respect to the DIRECTIONS of these crossings.
You see, it is not as easy as you perhaps think. Sorry for that.
Finally, here is my "conclusion" (in fact: derived from other sources):
The simplified Nyquist criterion is transferred to the BODE plot in the following way:
If the function L is stable (no RHP poles) and crosses the 0 db-line only once and if the phase crosses the 180-deg-line only once, you can use the phase/gain margin as a stability criterion.
More than that, if there are no RHP zeros (i.e. L is a minimum phase system), you may use only the slope of the magnitude to evaluate stability issues.
Regards