Stability analysis of dynamic interval type‐2 fuzzy control systems in frequency domain

Abstract

The present paper aims to analyze the stability of dynamic Interval Type-2 fuzzy control systems (IT2 FCSs) with adjustable parameters by investigating the existence of limit cycles based on the describing function (DF) method. To simplify the stability analysis, the following structured procedure is described. First, to avoid complex computation, a simple architecture of the IT2 FCS using two embedded Type-1 fuzzy control systems (T1 FCSs) is proposed. Then, the DF of IT2 FCS is obtained based on the DFs of embedded T1FCSs. Subsequently, integrating the stability equation and parameter plane approaches provides a solution to identify the limit cycle and the asymptotically stability regions. Moreover, particle swarm optimization (PSO) technique is utilized to minimize the limit cycle region. Other focus of this paper is on the stability margins analysis for robust design. For this purpose, a gain-phase margin tester is applied to determine the minimum Gain Margin (GM min ) and Phase Margin (PM min ) when limit cycles can arise. Finally, two simulation examples are given to verify the effectiveness of the proposed approach.

Membership function‐dependent predictive control for interval type‐2 Takagi–Sugeno fuzzy system

“…Takagi-Sugeno (T-S) fuzzy system has attracted abundant researchers' attention in last decades for its extraordinary ability to approximate nonlinearity at any precision through membership function connecting linear subsystems as in Takagi and Sugeno [1], allowing existing linear system theories [2][3][4][5] to be applied to nonlinearity system analysis. The failure to tackle membership function (MF) uncertainty for type-1 fuzzy set, on the other hand, necessitates a greater focus on interval type-2 (IT2) fuzzy model, which captures uncertainties via upper and lower MFs [6][7][8][9][10][11]. It was shown that the IT2 model performs better and has less conservatism in stability analysis than type-1 fuzzy model as in Li et al [12].…”

“…) where F i ∈ R n×s and C i ∈ R v×n are parameter matrices, 𝜔 ∈ R s is the unknown external disturbance satisfying 𝜔(k) ∈ L 2 (0, ∞), and 𝑦(k) ∈ R v is the interested output. With local fuzzy controller (10), rewrite (60) as…”

A unified general type‐2 fuzzy PID controller and its comparative with type‐1 and interval type‐2 fuzzy PID controller

“…In recent years, interval type-2 fuzzy sets have become a hot point for its secondary membership degree was set to 1, which simplified the type reduction procedure, and the commonly used type reduction algorithm for interval type-2 fuzzy sets was Karnik-Mendel (KM) [2] or enhanced KM (EKM) [3] algorithm. Interval type-2 fuzzy sets have been widely applied in many fields, like face recognition [4], time series prediction [5], pattern recognition [6], clustering [7], controlling systems [8][9][10][11][12][13], neuro-fuzzy systems [14], and so on.…”

Interval type-2 fuzzy aggregation operator in decision making and its application

“…Haghrah [16] proposed a novel Python toolkit fir interval type-2 fuzzy logic systems. Namad and Zare [35] analyzed the stability of interval type-2 control systems in frequency domain. Ontiveros-Robles et al [11] proposed a fuzzy logic controller according to performance and execution time.…”