Re: Basic Question

Pramit 'Jake' Sarma (psarma@che.iitb.ernet.in)
Tue, 22 Jun 1999 18:19:26 +0200 (MET DST)

It is often said that a fuzzy logic controller (FLC) is provides
"model-free" control. Well, that is itself at most fuzzy{true}. The
structure (rule-base (FRB), memb fn (MF), scaling gains (SG)) and their
tuning leads to a fuzzy model of the ideal controller, often notionally
expressed as the "plant inverse". But then this is the aim of every good
controller ... so in that sense, a FLC is very much related to other
methodologies. The double-edged advantage of the FLC lies within the
oft-quoted Universal Approximator property - given any [smooth] map
u = F[e], it is possible to find [tune] an FLC so that FLC[e] is as close
to F[e] as desired.

Another way is looking at these differences from 'conventional', or
crisp-like controllers. As Feijun Song mentions, there is this
single-point construction which 'slides' smoothly from one [crisp-like]
to another. As far as the good *old* PID-controllers go, it is interesting
to note that most 'standard' FLC's use a structure known as the
Fuzzy-PI[D], and there are a reasonable number of papers that "prove" the
equivalence: that an FLC is a nonlinear PI! But if one inspects Mamdani's
pathbreaking 1974/5/6 papers on FLC's, it is clear that the inspiration
for the 1st FLC was indeed the humble PI controller, to start with.

Fuzzy Logic can be called a "sub-science" since it is so universally
applicable, and provides a powerful alternative approach to crisp
problems, often complementing or simply outdoing them: Fuzzy {Regression,
Image Processing, Optimization, and many more}.

Pramit

On Mon, 21 Jun 1999, Mohammad Fazle Azeem wrote:

> Dear Fuzzy Member Hello!
> I am very much strange about the number of response of my comments according
> to my understanding of Fuzzy logic (enclosed at the last). Though I have
> mentioned in my comments about my needs. I received the comments from Dr.
> Feijun Song (enclosed after this message). I am sending this e-mail in the
> hope to receive some expert comments from the people working in this area. I
> think all fuzzy friends put their effort to stop me from going on forward on
> wrong track and guide me towards the right track. Thanks in advance for
> their precious time spending to read this e-mail and for making a response.
>
> M.F. Azeem
> EED, IIT Delhi,
> Hauz Khas, New Delhi-110 016,
> INDIA
>
>
>
> >From: Feijun Song <fsong@oe.fau.edu>***********************
> Hi, Azeem, you made a very good comment. the power of fuzzy logic in control
> field lies in its ablity to imcoorperate different methodologies into a
> systematic way, thus achieving better global performance which a single
> methodology can not do. For example, one can suggest: Fuzzy Sliding Mode
> Controller, or Sliding Mode Fuzzy Controoller, ( they are different ) to
> achieve broader operating range, while keeping the transition from one SMC
> to another SMC smooth.
>
> My comments********************
> Yes, Fuzzy Logic allows it. There is general misconception that Fuzzy logic
> is independent of other methodologies, i.e., classic and modern system
> approach. One can incorporate different methodologies in Fuzzy Logic. Fuzzy
> Logic gives different possible ways to combine methodologies for a
> particular situation. The best implementation of an Fuzzy Logic can be
> achieved by selecting a suitable type of model and Inferencing mechanism.
> This selection is depend upon the situation. For example around an operating
> point (in non-linear system) a PI controller (with particular set of
> parameter) works very well. As soon as either operating points or initial
> conditions get change we need to update PI parameters. With the use of Fuzzy
> Logic we can design a controller which can work for all feasible operating
> with the use of multiple PI controller. In this operation Fuzzy Logic
> function as supervisor in smooth switching from one PI controller to another
> PI controller. In a similar way we can incorporate different type of
> controller (not strictly PI) for a particular application. The broad
> spectrum of this suggestion is we can incorporate different methodologies in
> Fuzzy logic to get best feasible results. It is my view regarding Fuzzy
> logic after working on this subject since July'95. I am in need of
> correction or support of my view abou fuzzy logic. Both correction and
> support will be highly appreciable.
> Thanks
>
>
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Pramit "Jake" Sarma
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e-mail: jake_n_jazz@yahoo.com e-mail: psarma@che.iitb.ernet.in

Process Systems and Control
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