Class Of Fuzzy Logic Controllers Research Articles

Towards Systematic Design of General Type-2 Fuzzy Logic Controllers: Analysis, Interpretation, and Tuning

This article aims to provide a new perspective on how the deployment of general type-2 (GT2) fuzzy sets affects the mapping of a class of fuzzy logic controllers (FLCs). It is shown that an α-plane represented a GT2-FLC is easily designed via baseline type-1 and interval type-2 FLCs and two design parameters (DPs). The DPs are the total number of α planes and the tuning parameter of the secondary membership function that are interpreted as sensitivity and shape DPs, respectively. We provide a clear understanding and interpretation of the sensitivity and shape DPs on controller performance through various comparative analyses. We present design approaches on how to tune the shape DP by providing a tradeoff between robustness and performance. We also propose two online scheduling mechanisms to tune the shape DP. We explore the effect of the sensitivity DP on the GT2-FLC and provide practical insights on how to tune the sensitivity DP. We present an algorithm for tuning the sensitivity DP that provides a compromise between computational time and sensitivity. We validate our analyses, interpretations, and design methods with experimental results conducted on a drone. We believe that this article provides clear explanations on the role of DPs on the performance, robustness, sensitivity, and computational time of GT2-FLCs.

On the Connection between the Macvicar-Whelan Type Fuzzy Logic Control and Sliding Mode Control

ABSTRACT It has been recognized for some time that a class of fuzzy logic control is of the variable structure type. However, this has been concluded rather in an intuitive way and, to date, no rigorous proof is available to show the existence of the connection between fuzzy logic control and variable structure control. This paper addresses this issue and provides a rigorous proof that shows this connection for a class of fuzzy logic controllers whose rule base is of the Mac Vicar-Whelan type. In addition, the algebraic form of the switching function, inherent in this class of fuzzy logic controllers, is derived. This connection is also used to show the effect of the scaling factors of fuzzy logic control on system transient performance. Finally, a procedure is proposed in the purpose of systematically improving the transient performance of fuzzy control systems. To verify and illustrate the results of this paper, a numerical example is presented.

Analysis of the Algebraic Formula of a Class of Fuzzy Controllers

Fuzzy logic is considered as a form of artificial intelligence based on linguistic variables and rules. One of the most important applications of fuzzy logic is fuzzy logic control. Attempts to analyze the mechanism of fuzzy logic control have appeared in the literature and it has been recognized for some time that a class of fuzzy logic control is of the variable structure type. However, this has been concluded rather in an intuitive way and to date no rigorous proof is available to show the existence of the connection between fuzzy logic control and variable structure control. This paper addresses this issue and provides a rigorous proof that shows this connection for a class of fuzzy controllers.

Towards a paradigm for fuzzy logic control

The purpose of this paper is to lay a foundation for fuzzy logic control (FLC) design, constructing a class of fuzzy logic controllers that is suitable for a broad range of controls applications. Some scalar definitions in FLC are extended to the n-dimensional case, including vector fuzzy number and membership vector. A rigorous mathematical expression is given for the function g( x) (called the ‘reasoning surface’) manufactured by a fuzzy associative memory (FAM). For the existence and uniqueness of solutions in any closed-loop system with a fuzzy logic controller, it is shown that the FAM function g( x) must be Lipschitz: this places restrictions on the allowed rules in the FLC. It is argued that, for effective control design, the membership functions should not be uniformly spaced, the triangular membership functions generally suffice, and product inferencing should be used. Under these conditions, the FLC manufactures a piecewise-multilinear Lipschitz FAM function g( x) that is a generalized proportional-plus-derivative-plus-offset controller. The scalar and two-dimensional cases are studied in detail.