Re: Basic Question

Feijun Song (fsong@oe.fau.edu)
Thu, 24 Jun 1999 21:02:37 +0200 (MET DST)

function approximator point of view is also a key to understand why
generally a FLC can do a better job than a conventialal controller does.
Actually that a FLC is a universal apporximator is the basic assumption
in most FLC optimization and modeling techniques. We assume a Mamdani
and a TS type FLC can approximate any funcitons, then we use the Mamdani
and TS type fuzzy logic structure to model a system.

That's why TS type FLC was first proposed by Takagi & Sugeno
as a model identification technique.

I think Dr. Sarma, and Dr. Azeem have been pointing out straight forward
ways to understand why a FLC is better. I would like to mention a few more
based on my experience of FLC optimization for high order systems.( 4D ).

For 4D sytem, a convertional LQR needs a linearized model, and
the resulting LQR works very well when the system disturbance is small.
When the disturbance is large, a LQR can do nothing. This is esepically
true for 4D highly nonlinear systems. However, a FLC is capable of
generating a good control command in a large rangion of state space due
to the reason Dr. Sarma and Dr.Azeem has already mentioned. Moreover,
Assume we know all the optimal control commands on every points of a state
space, this control surface must be very nonlinear for 4D systems.
Can a LQR approximate this control surface? NO, only neural network or
fuzzy logic can possibly approximate this highly nonlinear but optimal
control surface. And a LQR can generate lots of oscillations around set
point, whereas a FLC can literally control without much oscillations

The only reason people do not like TS tyep FLC is that there are too many
parameters in it. Every rule is a P(I)D controller. For 4D system, the
selection of parameters are almost impossible. However, lots of people
suggested automatic ways to optimize a TS type FLC. A few I know can be
found in IEEE-FUZZY1992, IEEE-FUZZY1995,1996,1997, 1999 and IEEE-SMC1997.

Mamdani type FLC can be model free, but difficult to optimize, TS type
FLC is somewhat not model free, but easy to automatically optimize.

On Tue, 22 Jun 1999, Pramit 'Jake' Sarma wrote:

>
> 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
> [Home] [IIT-B]
>
> e-mail: jake_n_jazz@yahoo.com e-mail: psarma@che.iitb.ernet.in
>
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