1.2 A Bit of History

Complex industrial systems are controlled acceptably every day by human operators. Generally, these operators have no background in complex mathematical control strategies. Instead, they gain a “feel” for the system’s response to various control actions, and this “feel” allows them to manipulate the system effectively. One of the authors got a first-hand look at this method early in his career while working as a consultant for an oil and gas pipeline company. Consider the following account of his experience:

I was working for an oil and gas pipeline company in Atlanta, Georgia developing a computer model of transient waves in a gas pipeline pumping station. One day I wandered into a control room where an operator was overseeing an elaborate computer system that provided him with the information he needed to make control decisions. I began talking with him to find out just what his responsibilities were. I soon found that he was responsible for controlling all of the pumps and compressors on an oil and gas pipeline that ran from Houston, Texas up to somewhere in New Jersey. Needless to say, I was extremely impressed with this gentleman’s ability to manipulate such a complex system. Surely, I thought, he used some kind of computer program to help insure the safe and efficient operation of this pipeline. I was taken aback to learn that his education consisted of “finishing most of the tenth grade.” Being young and naive, I asked him if there wasn’t a computer program somewhere he could use to make his job easier. He told me that some professor from a local university had tried to develop one, but it used some high level math instead of good old common sense and experience. The computer program was a failure and was used only by the professor in his classroom.

Here was an operator with less than a high school education who was doing a job that a university engineering professor failed to do with computers and mathematical methods. This was an observation that had a major impact on the direction of this research.

When this project was initiated, the mineral processing industry presented an even more challenging setting than the pipeline industry. This was true for several reasons including: (1) the minerals industry, in general, was not highly computerized, (2) the minerals industry did not have adequate sensors for process control, (3) the ore input to the mineral processing systems varied a great deal over time, and (4) the mathematical models available were inadequate or unproven. Thus, the minerals industry provided a tremendous opportunity for developing innovative process control systems.

The “textbook” approach to developing a control system begins by developing a computer model (a transfer function) for the system to be controlled. Then, the transfer function is manipulated using various mathematical techniques. However, the authors had neither the time, the money, nor the inclination to develop and validate the transfer functions for complex mineral processing systems. Besides, are such transfer functions really necessary when human operators can achieve a reasonable level of control without them? In our investigation of this question, we discovered the writings of a wise man who had already been over this road.

Lofti Zadeh wrote the first paper on fuzzy set theory in 1965 (Zadeh, 1965). This paper introduced a system that allowed linguistic concepts to be manipulated by computers. It provided a mechanism for incorporating linguistic terms so familiar to human operators into computer programs. His arguments for adopting such an approach were centered around two basic ideas. First, as systems become more complex, the possibility of efficiently controlling them using traditional mathematical techniques is reduced. This occurs for numerous reasons including the failure to accurately model the complex systems over all-inclusive ranges of operations and because complex situations must be modeled in bits and pieces. Second, there are numerous situations in which a high price is paid for unneeded accuracy. The high price paid for accuracy is apparent in many day-to-day activities such as the task of parallel parking a car; there is no need to be precise, just get the car in the space without bumping into one of the neighboring cars. In a similar fashion the human process control operator is effective because he just gets the process controlled.

Zadeh’s early work was quite general. It did not focus on the use of fuzzy mathematics for process control, rather on its use in approximate reasoning tasks (Zadeh, 1968; 1971a; 1971b). This early work was quickly applied to fuzzy relational databases, image analysis, and decision support systems. It was not until Mamdani and his group of researchers (Mamdani and Assilian, 1975; Mamdani and Pappis, 1977) pioneered the use of fuzzy mathematics for control of laboratory scale problems, that the use of fuzzy logic for process control became a practical reality.