Fuzzy Control with Mamdani Systems
John H. Lilly · 2010
Mamdani fuzzy systems can be used to formulate compensators that are based on the user's common sense about how to control a system. Mamdani fuzzy systems have fuzzy sets in their rule consequents, as opposed to Takagi-Sugeno fuzzy systems, which have mathematical expressions in their rule consequents. For the ball and beam controller the inputs that would be needed are decided first, and then proper universes of discourse for all inputs and outputs are determined. This chapter introduces a method for conversion of PID controllers into fuzzy controllers. The equivalent fuzzy controller is exactly equal to the PID within its effective universe. This technique is useful because nonfuzzy proportional-integral-derivative (PID) controllers can be readily designed using well-known techniques. The chapter also introduces incremental fuzzy control, which prescribes the change in input rather than the input itself. Controlled Vocabulary Terms fuzzy control; fuzzy systems; three-term control