Fuzzy control systems are developed based on fuzzy set theory, attributed to Lotfi A. Zadeh (Zadeh, 1965, 1973), which extends the classical set theory with memberships of its elements described by the classical characteristic function (either “is” or “is not” a member of the set), to allow for partial membership described by a membership function (both “is” and “is not” a member of the set at the same time, with a certain degree of belonging to the set). Thus, fuzzy set theory has great capabilities and flexibilities in solving many real-world problems which classical set theory does not intend or fails to handle. Fuzzy set theory was applied to control systems theory and engineering almost immediately after its birth. Advances in modern computer technology continuously backs up the fuzzy framework for coping with engineering systems of a broad spectrum, including many control systems that are too complex or too imprecise to tackle by conventional control theories and techniques
Background: Fuzzy Control Systems
The main signature of fuzzy logic technology is its ability of suggesting an approximate solution to an imprecisely formulated problem. From this point of view, fuzzy logic is closer to human reasoning than the classical logic, where the latter attempts to precisely formulate and exactly solve a mathematical or technical problem if ever possible.
Motivations for Fuzzy Control Systems Theory
Conventional control systems theory, developed based on classical mathematics and the two-valued logic, is relatively mature and complete. This theory has its solid foundation built on classical mathematics, electrical engineering, and computer technology. It can provide rigorous analysis and often perfect solutions when a system is precisely defined mathematically. Within this framework, some relatively advanced control techniques such as adaptive, robust and nonlinear control theories have gained rapid development in the last three decades.
However, conventional control theory is quite limited in modeling and controlling complex dynamical systems, particularly ill-formulated and partially-described physical systems. Fuzzy logic control theory, on the contrary, has shown potential in these kinds of non-traditional applications. Fuzzy logic technology allows the designers to build controllers even when their understanding of the system is still in a vague, incomplete, and developing phase, and such situations are quite common in industrial control practice.
Key Terms in this Chapter
Fuzzy Control: A control method based on fuzzy set and fuzzy logic theories.
Fuzzy Logic: A logic that takes on continuous values in between 0 and 1.
Fuzzification: A process that converts conventional expressions to fuzzy terms quantified by fuzzy membership functions.
Defuzzification: A process that converts fuzzy terms to conventional expressions quantified by real-valued functions.
Fuzzy Set: A set of elements with a real-valued membership function describing their grades.
Fuzzy Membership Function: A function defined on fuzzy set and assumes continuous values in between 0 and 1.
Fuzzy System: A system formulated and described by fuzzy set-based real-valued functions.