Design of a Single-input Adaptive Fuzzy Logic Controller using a Switching Hyperplane

Most fuzzy logic controllers (FLCs) for minimum phase plants use an UNLP (Upper Negative and Lower Positive) or UPLN type control rule table. This property allows design of a single-input FLC using a sole input fuzzy variable, which is called the SFLC (single-input FLC). It greatly simplifies the design procedure of the conventional FLC and has many advantages. However, it is still difficult to adapt to varying operating conditions. We here design a single-input adaptive fuzzy logic controller (SAFLC) using a switching hyperplane introduced in sliding mode control. In the proposed SAFLC, some parameters of membership functions characterizing linguistic terms of fuzzy rules are adjusted by an adaptive law that directly incorporates linguistic fuzzy control rules into the controller. We also prove that 1) the closed-loop system is globally stable in the sense that all signals involved are bounded and 2) its tracking error converges to zero asymptotically. We perform computer simulation using an inverted pendulum system.