I want to take advantage of this occasion to tell you my experience with Fuzzy Logic. I am in charge of an R&D department where we develop spark erosion generators. Our company manufactures electrical discharge machining (EDM) tools.
As you might know, these machines are used to form a negative shape in a very hard metal (carbide or hardened steel), starting from a graphite or copper electrode (easy to machine), or using a traveling wire as a cutting electrode. We apply a voltage between the electrode and the workpiece, in a dielectric oil bath. As soon as the current flows, a plasma channel builds up, and spark by spark, we machine the workpiece, leaving the electrode almost intact. The result is a mold, die, or punch to manufacture almost anything and everything.
Every object made of plastic, and many made of metal come from this process, e.g.: cellular phones, TV sets, connectors, coins, microstructures, integrated-circuit lead frames, surgical tools, almost every automotive part, fuel-injection nozzles, turbine blades, etc. The EDM process is a nightmare to control. One has to control the gap width (the distance between the electrode and the workpiece) very tightly, otherwise the process degenerates into an arc, damaging the electrode, and burning the oil—and eventually the factory. The energy density involved is very high, typically 105 to 107 W/mm2; therefore we have less than 1 ms to control the gap width.
The process is rather slow (typically 10 to 500 mm3/min. stock removal). Therefore, it is very important to use good process control, to maximize the machining speed. So, usually several parameters are controlled at the same time (gap-width setpoint value, pulse frequency, pulse shape, voltage, current, flushing, etc.).
To make things worse, in spite of several efforts (Texas A & M University, Technical University Aachen) to build a process model, we still have no useful macroscopic model to apply in the control system. Due to the always-changing local geometry, the EDM process is highly nonlinear, stochastic, and non-stationary.
In 1993 we thought about using Fuzzy Logic to control the EDM process, in absence of better methods. Up to that time, we had been using analog controllers, then digital ones, utilizing the Ziegler Nichols criterium to approximate the PID coefficients. (Better than nothing.)
This kind of controller worked OK, but the Fuzzy system, after about six months of optimization, gave better results. In the most difficult machinings, we could improve the speed by 20% to 200%. This is probably because we used rules that came from the experience of our skilled operators to fine-tune the Fuzzy rule base, according to the machining context, i.e.: roughing, finishing in a deep cavity, bad flushing conditions, etc.
Since then we have sold about 2000 EDM machines that perform the most varied and difficult machining tasks, and we can conclude that in our case, Fuzzy Logic helped us to improve the process control. Having said this, I agree with you that in most cases, Fuzzy Logic is not better than a properly-designed traditional controller, and I never use it if there is an alternative.
My congratulations to you, Mr. Boccadoro! It sounds like you have used Fuzzy Logic (FL) to solve some serious nonlinear problems. As I suspected all along, when the problems are very nonlinear, and no mathematical models have been found—maybe if you work really HARD, using FL, you can get the advantages that FL provides—which is completely different than just saying "FL is easy to do."
I bet that team of engineers that worked six months to get it to work well, did not think it was "easy." I am also pleased to note your observations that working experience in such a process is valuable to get the FL controller to work well. Mindless promoters of FL who say that you do not have to know anything about the process are just foolish. I'm delighted to publish your letter, as a sanity-check on FL. Note that a U.S. Patent has been issued on this technology. Great work!—RAP
All for now. / Comments invited!
RAP / Robert A. Pease / Engineer
[email protected] team.nsc.com—or:
Mail Stop D2597A
P.O. Box 58090
Santa Clara, CA 95052-8090
P. S. There are a couple loose ends to tie up on the 1-MHz VFC Analog Supplement column packaged with this issue. I neglected to mention the nonlinearity I observed. After I put in the LM741 buffer, the linearity was about 5 ppm of Full Scale PLUS about 0.03% of signal. Thus, at 5.00000 V, F was about 500,150 Hz, referred to 1,000,000 Hz at 10.00000 volts.
I could get the tempco down to about 40 ppm/°C by shunting down the 3-k resistor listed at "Tempco Trim." I should mention that the critical 50 pF capacitor (in series with 1 k) was a silver-mica, which typically has 50 ppm/°C. You could use an NPO or COG ceramic for fairly similar results. Can I invent a trick circuit to improve the linearity even further? Yeah, I could probably feed a small fraction of VIN, into the input of the LM741. Ask me for details.
And there was one minor goof in the published schematic. If you want to put in a negative input signal, through the 10-k pot and the 40-k resistor, this works fine, as shown. But if you want to put in a positive VIN, then you have to add a 4.02 k resistor to ground, from the negative input of the first amplifier, to get the correct gain and scaling. The original hand-drawn schematic had this 4.02 k, and the actual circuit had this resistor built in, but I did not check the computerized schematic closely enough, until an hour after the column went to press. Just goes to show how checking is not easy. If I had taken a red pencil and checked off each item on old and new schematics, I would have noticed the discrepancy. Sorry. /rap