Fuzzy Semigroups

The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. The book concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. Basic results on fuzzy subsets, semigroups, codes, finite state machines, and languages are reviewed and introduced, as well as certain fuzzy ideals of a semigroup and advanced characterizations and properties of fuzzy semigroups.In this book, modeling and control design of electric motors, namely step motors, brushless DC motors, and induction motors, are considered. The book focuses on recent advances on feedback control designs for various types of electric motors, with a slight emphasis on stepper motors. For this purpose, the authors explore modeling of these devices to the extent needed to provide a high-performance controller but at the same time amenable to model-based nonlinear designs. The control designs focus particularly on recent robust adaptive nonlinear controllers to attain high performance. It is shown that the adaptive robust nonlinear controller on its own achieves a reasonably good performance without requiring the exact knowledge of motor parameters. While carefully tuned classical controllers do often achieve required performance in many applications, it is hoped that the advocated robust and adaptive designs will lead to standard universal controllers with minimal need for fine tuning of control parameters.