From: dlgerber@eos.ncsu.edu (DARRELL L GERBER)
Subject: Re: WHEN and WHY should I use FUZZY logic?
Organization: North Carolina State University
Date: Fri, 22 Jan 1993 21:27:49 GMT

In article <C15uAt.8nH@cpqhou.se.hou.compaq.com>, pipkinsj@cpqhou.se.hou.compaq.com (Jeff Pipkins ) writes:
|> 
|> There seem to be plenty of answers to the question of WHAT fuzzy logic
|> is, and HOW it works.  There are several good primers that provide
|> a good introduction to those questions. 
            
		(stuff deleted)

|> 
|> I'm trying to keep an open mind about this whole fuzzy thing, but I just
|> can't imagine a situation where I could benefit from it.  I'm willing to
|> assume that the problem is my ignorance...  So, enlighten me!

One reason for using Fuzzy Logic Controllers which hasn't been emphasised enough
is that you don't need any kind of model to apply it.  This may not seem like a
big deal for simple systems (in fact, if compared with standard PD control of a
simple pendulum it is much slower and more complex) but if you consider highly
non-linear and coupled systems (such as robots) it is very fortunate to not have
to develop a mathematical model of the system.  

Another important consideration is how easy (relatively) it is to make the basic
fuzzy logic controller adaptive.  In fact, I am currently working on developing
an adaptive fuzzy logic controller which uses a second fuzzy logic controller as
the basis for the adaptation routine.  The beauty of this is that you still
don't need any model or parameter identification routine.  Unfortunately, how do
you prove it is stable and converges??  I don't know!?!?

One other thing I haven't seen mentioned is how the rule base in fuzzy can be
chosen to resemble other types of controllers.  For example, consider the simple
PD controller.  If you plot the resulting output as a function of the error in
position and the error in velocity (e and edot) you will find it is just a plane
whose orientation is governed by the proportional and derivative constants. 
Now, place a grid over the plane described by the e and edot axes and create 
fuzzy sets centered at the intersections between the grid and the axes.  The way
to make a fuzzy rule base to resemble PD control is create a rule for each point
on the grid of the form:

	IF (applicable fuzzy set on e axis) AND (applicable fuzzy set on
	edot axis) THEN (value of PD plane directly above the intersection)

This may sound pretty confusing but it is much easier to understand if you have
a picture.  This example, however, is good to get the basic idea but the 
concept is valid no matter how many degrees you have (this was 3D) and what
type of control surface (or hypersurface) you are trying to match.  

You may be wondering why anyone would want to use this if they could use the
original controller.  It may not be obvious but if you are using an adaptive
fuzzy controller you can start with a rule base found from this method and then
let the adaptation routine "tune" it to what the best control surface for that
particular system.  Again, no models needed!!

------------------------------

dlgerber@eos.ncsu.edu
Department of Mechanical and Aerospace Engineering
North Carolina State University

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