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From: bytex!bytex.com!mackw@uunet.uu.net
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Subject: Re: Fuzzy control-illusion or future 
Date: Thu, 05 Jan 95 18:04:49 PDT
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In article <3eeaum$74l@josie.abo.fi>, <jpensar@abo.fi> writes:
> Also, if we give up a mathematical way of describing performance, then
> how would we determine if your fuzzy controller is as good as my spline 
> controller?

An important point to remember is that the mathmatical model is not the
real world!  The question is not whether an implementation comes closer
to a mathmatical model, but whether is is possible or feasible to develop
a mathmatical model in the first place.  The advantage of fuzzy logic 
control is that it can be used for systems which are too complex for a
mathmatical model.
 
> A relevant question here is "Is human logic enough for control?". 
> For simple SISO problems without hard performance requirements, I 
> would guess it's enough, but for complex, possible unstable MIMO 
> systems I would say no. A human operator can not know that the best 
> way to control a fictive process is:
>    When a step in feed composition occurs, You should
>    - For the first minute, increase the steam flow to the reboiler
>      (stepsize*0.35) kg/s^2
>      while decreasing the reflux rate (stepsize/10)kg/s^s
>    - after one minute sharply drop the flow to reboiler with 20 %
>      while still increasing the reflux.
>    - When the first sight of temperture increase on tray 12 is noticed
>      decrease the reflux flow with (stepsize/5)kg/s^2 until top
>      compositon settles.
>    - etc etc...
> Instead he will know that, ok, for a step in feedcomposition of 5%, 
> decrease reflux with, say, 2kg/s and increase steam flow with 4kg/s.

The point is that in many control systems, these very precise rates you
give are unknown and often they are not constants but controlled by some
complex function.  It is *standard control theory* approaches which make
such simplifying assumptions in order to create a simple model.  Sure, the
eventual result may match the model, but that does not imply the model
was correct!

> The big advantage of fuzzy control is that it nicely maps linguistic 
> knowledge to an input-output approximation. This may for simple
> process dynamics give "good enough" performance. When the dynamic 
> properties of the process gets hairy, no human operator will know 
> the best way to control the process. Here we need other tools for 
> control design and analyze. 

If the process is beyond the ability of a human operator to know how to 
control, how would it be possible to for a human to know how to create
a mathmatical model of the control process?  Sure some processes may
require response times too quick for a human to operate, but that is
quite different from saying that it is too complex for him to understand.
In fact, in complex control situations, the problem is often the opposite;
the mathmatical model does not understand how to react under all
circumstances and human intervention is required in these cases.

Best Regards,
Wayne Mack
