A comparative investigation of the utility of dynamic compensation in fuzzy control
Harold W. Lewis · 1995
The broadest purpose of this dissertation is to present a view of the fuzzy control methodology that emphasizes its relationships with other technologies. Thus, three introductory chapters contain detailed, conceptual treatments of conventional control theory, artificial intelligence, and fuzzy set theory; and two further background chapters discuss how these three bodies of knowledge tie together to provide a clearer understanding of fuzzy control in its many, varied forms. These chapters also contain a somewhat original treatment of the mathematical formalisms that underlie approximate reasoning by linguistic variables and fuzzy logic. This treatment is arguably much more straightforward than the one usually found in the literature. However, a proof is also given to show that the two treatments are equivalent in results. This approach flows naturally into the second half of the dissertation which describes original empirical research. This is perhaps the most methodical research to date that is addressed specifically to the question of how valuable dynamic compensation is in the context of fuzzy control designs. The essence of the behavior of an actual, very small steam engine is captured within a computer by means of neural approximation networks. Next, fuzzy control devices, with and without various forms of dynamic compensation, are designed to control the steam engine. The various designs are optimized by means of a genetic based auto-tuning technique. Finally, the control designs are rigorously tested and compared by simulation within the computer. The results indicate that a derivative term is extremely valuable in fuzzy control, not only because it improves performance, but also because it makes the controller less sensitive to possible imperfections in its design. An integral term can also improve performance, but only under some conditions, and only if some care is taken in optimizing the design. Because auto-tuning techniques are not readily available for fuzzy control, one can conclude that most fuzzy control designs in the future should use both derivative and integral terms.