Some new performance definitions of second-order fuzzy systems

Abstract

The mathematical models are usually considered for the assessment of a dynamical system performance. Using such models often is based on an assumption which takes all the system parameter values as crisp values into account. However, the parameter values may not be always determined exactly. Since fuzzy logic has been well known as an effective tool in modeling uncertainty, in this paper, fuzzy numbers are used in modeling of dynamical systems. In this paper, concentrate on second-order dynamical systems with fuzzy parameters as they play a major role in many aspects of control theory. New performance definitions such as fuzzy rise time, fuzzy settling time, and fuzzy maximum overshoot are presented. The new definitions for such systems provide a more comprehensive view of the system output which helps for designing a better control. Also, the solutions of an RLC circuit and intelligent transformer with fuzzy parameter based on these definitions are considered.