Stability analysis of dynamic interval type‐2 fuzzy control systems in frequency domain. Issue 6 (5th August 2020)

• Record Type: Journal Article
• Authors: Namadchian, Zahra; Zare, Assef
• Is Part Of: Asian journal of control. Volume 23:Issue 6(2021)
• Page Start: 2729
• Page End: 2739
• Publication Date: 2020-08-05
• Subjects: describing function -- gain margin -- Interval type‐2 fuzzy control systems -- limit cycle -- phase margin -- stability; Automatic control -- Periodicals; Control theory -- Periodicals; 629.805
• DOI: 10.1002/asjc.2407
• Languages: English
• ISSNs: 1561-8625

Abstract

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 ( G M m i n ) and Phase Margin ( P M m i n ) when limit cycles can arise. Finally, two simulation examples are given to verify the effectiveness of the proposed approach.