2.4 Review and Preview

This chapter has provided a step-by-step procedure for developing fuzzy control systems. This technique was demonstrated on a very simple liquid level system for which the reader could easily write some general, yet effective control rules. The idea of fuzzification via fuzzy sets was introduced (although hopefully it was done so subtly that you barely noticed it) along with the idea of defuzzification (simply taking a weighted average of the actions prescribed by the various rules). Results were provided to demonstrate that a control system could in fact be developed for the liquid level system using the guidelines presented.

When this material is presented to students, it seems to create as many questions as answers: (1) what if the rules are not readily apparent? (2) how do I get the membership functions? do their definitions affect the performance of the control system? (3) what if I don’t have a computer model to develop my controller? and (5) what time is this class over? (there is always at least one in every group). Hopefully, you have some of the same questions and more (although the fourth question is not allowed from readers). Please, we will address these questions and plenty more we ran into during the course of the project. However, we feel there is now a more pressing need: to ensure that this simple step-by-step procedure for FLC development will work in more complex problem environments. Thus, in the next chapter we attempt to instill some confidence in this very straightforward approach by using it to develop a controller for a more difficult system, a cart-pole system that has become a standard in the computational intelligence-based controls community.

References

Bartolini, G., Casalino, G., Davoli, F., Mastretta, M., Minciardi, R., and Morten, E. (1985). Development of performance adaptive fuzzy controllers with application to continuous casting plants, Industrial Applications of Fuzzy Control (M. Sugeno, ed.), North-Holland, Amsterdam, p. 73.

Karr, C. L., and Gentry, E. J. (1992). Real-time pH control using fuzzy logic and genetic algorithms. Proceedings of Annual Meeting of the Society for Mining, Metallurgy, and Exploration, Phoenix, AZ, February, 1992.

Kickert, W. J. M., and Van Nauta Lemke, J. R. (1976). Applications of a fuzzy controller to a warm water plant, Automatica, 12: 301–308.

Larkin, L. I. (1985). A fuzzy logic controller for aircraft flight control, Industrial Applications of Fuzzy Control (M. Sugeno, ed.), North-Holland, Amsterdam, p. 87.

Shah, I., and Rajamani, K. (1988). Fuzzy logic controller: Application to liquid level system. Proceedings of IFAC Symposium on Automation in Mining, Metallurgy and Metals Processing, Johannesburg, pp. 186–192.

Waterman, D. A. (1989). A Guide to Expert Systems, Addison-Wesley, Reading, MA.