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I was just reading about the anti-lock brake system example on the wiki page for fuzzy control system. The principle seems to be simple: instead of just assigning a SINGLE category (cold, cool, nominal, warm or hot) to the temperature of the brake, it translates the temperature into a continuous scale (fuzzy set), like 70% cold and 30% cool.

I can see the advantage of this over the 0-1 logic because now the input is smoother than the 0-1 logic and so the output will also be smoother. But if you have the temperature available, which is already in a continuous scale, why not just control directly based on the temperature? Why do you need the extra step to convert the temperature into fuzzy set and then do the control?

I noticed fuzzy control seems to be a hot topic a couple of decades ago. So maybe it's just because the controllers (in applications like cars and washing machines) were only capable of controlling based on rules rather than doing PID control?

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In your example it mentions that the micro controller for the ABS is making decisions based on the "states" of the brakes, one of which is temperature. The micro controller may be be applying different control gains depending on the states, which is a form of adaptive control.

A simple PID controller may not be able to be tuned to handle (perform well enough) a wide range of states, so there is some advantage to using FL in combination with traditional methods. FL is by no means the only way to do adaptive control, but it is fairly easy to implement.

So to be more direct in answering your question, it sounds like whoever designed the ABS in that example chose not to implement control on a continuous range of input states (i.e. temperature) because it was a lot easier than coming up with an alternative (adaptive controller, gain scheduler, or PID).

There can be a lot of complex issues when designing a controller that has to deal with a system that can alternate between linear and non-linear response regions or uncertainty in observations. There is some simple beauty to a FLC in that it can be easily setup to deal with such situations.

For an interesting read, try this paper.

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