THE BEST OF BOB PEASE

I became an instant "expert" on fuzzy logic (FL) in May of 1993, after questioning¹ the advantages claimed for it -- too many were preposterous and made no sense. Now after writing five more columns on FL^2-6, lecturing, and receiving many thoughtful letters, I am not much more of an expert on doing FL than in 1993. 

But, no problem: most people publishing papers touting FL as having great advantages over conventional systems know less about good conventional systems than I do about FL. And a lot of my bold statements about FL been confirmed. For example, when an FL system claims to show great advantages over a conventional system, the advantages arise because the conventional system was badly done, or because it was heavily nonlinear. 

So-called experts make silly claims for FL: "An elevator not based on FL runs at constant speed until it reaches the destination, then comes to a rough stop."⁷ Absurd! Then an FL "expert" on the radio⁸ claimed that the 1993 Saturn automobile's automatic transmission was redesigned with FL. Daniel McNeill, author of a collection of platitudes and puffery about FL,⁹ stated that on steep upgrades, the transmission used FL to cut out "hunting" and excessive shifting up and down. He said that ordinary automatic transmissions "always shift at the same speed," but by using FL, they can be made to shift at different speeds -- poppycock!! Well, the Saturn's transmission was improved, but it did not use FL to improve its behavior on upgrades.¹⁰ Designers used FL only to provide downshifts on downgrades. Every example of FL included bad thinking and untrue statements -- which made me very suspicious! 

Several people recommended the Sendai train as an excellent example of FL, providing smoother acceleration, faster speed, and better energy economy in a practical system. The Sendai train actually provides worse energy economy;⁴ it only appeared to give better economy due to a flawed 1985 computer analysis. In addition, the only published research¹¹ about the train appeared before it began operation. So all FL enthusiasts must stop claiming that the Sendai train uses less energy. It is a very good, smooth train, and very well engineered, but it cannot travel faster between stations and still consume less energy. This is not because FL is bad, but just because the train provides smoother acceleration. 

Several other people have pointed out that, even today, most technical papers on FL show trivial or "toy" examples, not real-world examples. Such papers still set up "straw men." Also, they are written in esoteric symbols and couched in obscure, scholarly phraseology -- and thus are incomprehensible to most serious students or practitioners of FL. 

Most FL controllers respond only to proportional and derivative terms⁵ and do not have integral response. So a true PID (proportional-integral-derivative) controller, whether analog, digital, or FL, can achieve better accuracy and better dynamic response. These days, few engineers know what PID control⁶ is or why it is useful. 

Some authorities (notably Bart Kosko) argue that when we go from two parameters to three, and use seven rules in each dimension, the number of fuzzy rules increases grossly, from 49 (7²) to 343 (7³), for example. In most cases, that are more or less linear, however, we can use three or five rules, rather than seven. if we add an integral term to the main (proportional) parameter, we may add a small number of new rules, while easily accommodating a third or fourth parameter. So, conversion of an FL to a full-PID controller may require only a few more rules, leading to greatly improved performance. 

Dave Brubaker, a serious practitioner of FL, showed¹² the advantages of using PID control in FL. And Adaptive Logic (San Jose, California,) has new software that facilitates the design of PID FL controllers. This can be powerful: a full-PID controller that adds FL's ability to handle nonlinearities. 

So what else are we learning about FL? For one, there is still a lot of hype. Ads insist that we'll prefer a $249.95 FL electric razor or a $99.99 FL electric toothbrush. Maybe; I'll wait to see what Consumer Reports says. Meanwhile, there are still many impractical promoters of FL -- balanced by a number of excellent, practical ones. 

Such a case comes from Constantin von Altrock of Inform¹³ (Oak Park, Illinois). A team from Inform built an autonomous racing car with a 1-hp electric motor for its 10 lbs. of weight, with a complete computer on board, plus an FL pattern recognition system. They put tape down on a parking lot to indicate a race track, so the car could sense its location on the track and when it was coming up to curves. 

After a couple of hours writing software, the team got the car to move around the track -- but it performed poorly, skidding badly and driving stupidly. Yet, two weeks later, the software improved, and the car could really drift the corners and race competently. Impressive! Next, the team threw boxes (with tape on the edges, for visibility) onto the track, and the car dodged the boxes and kept racing! Bravo! This may not yet be useful, but it is a virtuoso performance, nontrivial, and not feasible with conventional computers. It can't even be done with op amps! Surely such capabilities will soon prove useful. 

Enthusiasts make positive claims for process controllers using FL added to or instead of conventional PID controllers. However, people write saying that, despite these positive claims, FL controllers did not work as well as a good PID controller, in their particular application. Still, a marketeer at Omron Electronics, (Schaumburg, Illinois) pointed out that a good controller does cost extra with added FL; and these augmented controllers are selling pretty well. Why would people pay more? Because, in some applications, the ones with FL really do work better. This fact is compelling. As Jay Last (a Teledyne founder) says, "The only valid market survey is a signed purchase order." 

At the 1994 Fuzzy Logic conference, the most impressive demonstration had a ping-pong ball floating atop a column of moving air in a vertical plastic cylinder. An FL controller moved the ball between three levels. This problem is fairly nonlinear and not easily controlled, even with a good detector to indicate the ball's location. (Most FL examples never mention the sensors used, or the sample rate, which can be very important.) Two of the movements were smooth, but the third overshot badly and oscillated. After a few hours, the third transition was alright, but the second one was poor. They never got all three transitions working correctly. So, while it is possible to optimize an FL system, doing so is difficult, despite some FL enthusiasts' claims that optimizing an FL system is easy. Claims that PID is difficult to use are similarly untrue.¹⁴ 

An article about balancing a ball on a tilting beam¹⁵ claimed that an FL controller, using only a 486-based computer, was faster and settled better (compared to an untrained human operator). The published plot of the ball's motion was unbelievable because it showed that the ball sometimes did not accelerate after the beam tilted and sometimes accelerated when the beam did not tilt. In addition, the ball had a 100-percent overshoot five times before settling. And despite these poor results, the authors insisted that they got better performance using FL and did not have to provide a mathematical model for the system. When confronted,¹⁶ the authors insisted their design was good,¹⁷ but did not explain the erratic data. 

I built my own ball-on-a-beam balancer and used a mathematical model. The ball's velocity is the integral of the tilt, and when a ball rolls, its position is the integral of its velocity. Thus, the ball's position is a double integration on the beam's tilt. I designed the controller in a couple of hours using scrap paper and pen -- not a computer. The design uses four op amps (LMC660) as integrators and differentiators. 

This design ran on the first try. While its motion is not yet optimal, the ball still settles promptly without even 5 percent of overshoot, in about 6 seconds for a 20-in. motion. Thus, four op amps (costing less than $1) can, in a thoughtful application, outperform a $1,500 personal computer. This works because a good model exists for the rolling ball (rather than pretending to be better off without any model). 

A while back, Lotfi Zadeh and I discussed ball-on-beam balancing. He thought he could make a ball roll on a lossy tilting surface (such as carpet) with humps to hinder the ball's free roll, and could even make it arrive on target at a particular time. I said that was possible with op amps, too, but he could surely do it better, because FL is very good for nonlinear cases. 

Then Lotfi spoke of a colleague who still dislikes FL. This person said, "Lotfi, I hope I live long enough to see you invited to the White House, where the President will present you with a medal 'For fooling the Japanese into thinking that fuzzy logic is a good idea'." It was really charming that Lotfi had such a fine sense of humor, and could tell a joke on himself, on such a serious topic! 

I invite your comments. 

Robert A. Pease
Mail Stop D2597A
National Semiconductor
P.O. Box 58090
Santa Clara, CA 95052-8090
E-mail: czar44@me.com 

References 

References 1-6 and 15-17 available from the author -- Ed.

2. R.A. Pease, "What's All This Fuzzy Logic Stuff, Anyhow?," Electronic Design, May 13, 1993, pp. 77-79.   

3. R.A. Pease, "What's All This Fuzzy Logic Stuff, Anyhow (Part II)?," Electronic Design, Nov. 1, 1993, pp. 95-98.   

4. R.A. Pease, "What's All This Fuzzy Logic Stuff, Anyhow (Part III)?," Electronic Design Nov. 11, 1993, pp. 105-108.   

5. R.A. Pease, "What's All This Acceleration Stuff, Anyhow?," Electronic Design, Nov. 7, 1994, pp. 63-64.   

6. R.A. Pease, "What's All This Refrigerator Stuff, Anyhow?," Electronic Design, Dec. 16, 1994, pp.111- 113.   

7. R.A. Pease, "What's All This PID Stuff, Anyhow?," Electronic Design, June 26, 1995 (special issue on Analog Applications).   

8. Electronic Design, June 25,1992, p. 37.   

9. Interview with Daniel McNeill, "Marketplace," on NPR's KQED-FM, 6:49 p.m., Mar. 23, 1993, Marketplace Radio, Los Angeles, Calif.   

10. D. McNeill and P. Freiberger, Fuzzy Logic, Simon & Schuster, Old Tappan, N.J., 1993.   

11. Automotive Industries, Feb. 1993, pp. 149-150.   

12. S. Yasunobu and S. Miyamoto, "Automatic Train Operation System by Predictive Fuzzy Control," Industrial Applications of Fuzzy Control, Elsevier Science Publishers, New York, 1985, pp. 1-18.   

13. D. Brubaker, "Design a Fuzzy Set-Point Controller," EDN, Jan. 5, pp. 167-170; Feb. 16, pp. 163-166; and Mar. 16, 1995, pp. 133-136.   

14. INFORM GmbH, "Advanced Fuzzy Logic Control of a Model Car," J. Fuzzy Sets and Systems, Elsevier Science Publishers, New York, 1994.   

15. QuickMotion, Pro-Log, Monterey, Calif.   

16. H. Li and Y. Ji, "Fuzzy-Logic Tools on Tap for IC Wafers," IEEE Circuits and Devices, Mar. 1994, pp. 30-35,   

17. R. Pease, "Letters to the Editor," IEEE Circuits and Devices, Sept. 1994, pp. 4-6.   

18. H. Li, "Letters to the Editor," IEEE Circuits and Devices, Sept. 1994, pp. 6, 19.

Originally published in the August 1995 IEEE Micro Magazine. 

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