Bode plot of system can be used to explain its stability instead of pole zero plot? Bode plot can be used in paper for stability analysis?
www.chemengr.ucsb.edu/~ceweb/faculty/seborg/teaching/SEM_2.../Chapter_14.ppt
Dear Arshad,
Bode plot can give you a lot of information regarding the stability of the system, more precisely the phase and gain margins. That you can identify them from the Bode plot or directly from the Matlab code:
[Gm,Pm,Wgm,Wpm] = margin(sys)
Best wishes,
As Tamir stated, a Bode plot will allow you to determine the gain and phase margins of your system. A pole-zero plot gives you more information than just stability, it allows you to understand what the response of the system will be from the locations of the poles. See section 1.2 of this: http://web.mit.edu/2.14/www/Handouts/PoleZero.pdf
Dear Arshad (and All),
As I wrote for another similar topic, Bode plot is the simplest and the best... for simple systems, when the open-loop system is stable and the plots look close to straight lines.
However, if the system is more complex, and the many poles and zeros make the gain and phase plot lines move up-and-down, it is almost mission impossible to get any conclusion from Bode plots, not to even mention open-loop unstable systems.
In such cases, one would have to go and plot Nyquist plots and see what happens around the special point (-1,0). However, because the gain in Nyquist plots is linear, it may go up to tens of thousands, while we are interested in (-1,0).
The compromise that I think is the best, is Nichols plot, where the gain, like in Bode plots, is at logarithmic scale. However, because it puts the gain and phase on same plot, it gives you a more understandable picture. After you plot a few systems and get some experience, you understand that the gain and phase may jump at will as long as their plot leaves the region around the center point at 0 dB and -180 degrees free.
As these days in MATLAB you just have to write nichols (or bode or nyquist) to get the plot, it is not difficult to plot them and compare them all, to make your own impression.
Have Fun!
Itzhak
Thank a lot all of you. The feedback from all of you was really informative and conclusive. I really appreciate you guys feedback.
Stay blessed all.
Warm Regards
I only can support Itzhak Barkana´s recommendation regarding the Nichols plot. It`s really versatile.
Dear Arshad and other contributors,
I think the remarks are relevant. Pointing out Nichols chart (by Itzhak) was really nice. Let me add a few remarks which could turn out to be important. I mention them from many years experience in class room... I know these are recurrent doubts.
1) Bode diagrams are one way of graphically representing the frequency response of a LTI (linear time-invariant) system, which is by definition, the Fourier Transform of the impulse response of the system;
2) Although Matlab will provide a Bode Plot for an unstable system, such a plot should not be interpreted as a frequency response, because an unstable system does not respond sinusoidally to a sinusoidal input. Mathematically, the impulse response of an unstable system is not an absolutely integrable signal and the corresponding Fourier Transform does not converge.
3) Out of technicalities and into stability... Supose a system with frequency response G(jw), if it has a frequency response then it is stable by definition;
4) Now what seems to be implied in your question is how to use a Bode Diagram of G(jw) to establish the stability of G(jw)/1+G(jw), which is the frequency response of the closed-loop system. Practically all the answers given were provided assuming this (which is the most natural interpretation).
5) Making a long story short: if the system is open-loop unstable, then Bode Diagrams are not the best way of addressing stability either of the open or of the closed-loop. If the loop transfer function is open-loop stable, then, yes, you will find the answer to the stability of the closed-loop system by measuring the gain and or phase-margins.
6) This is valid for both, continuous- and discrete-time systems, although we cannot use the concepts of asymptotes (straight line approximations) to plot Bode Diagrams for discrete-time systems.
Regards.
Luis
By finding phase margin and gain margin you can know the stability of system.
If both are positive system is stable otherwise not.check this link
http://www.mit.edu/afs.new/athena/course/2/2.010/www_f00/psets/hw3_dir/tutor3_dir/tut3_g.html
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