Fuzzy modeling and control of a class of non‐differentiable multi‐input multi‐output nonlinear systems

• Published in: Asian journal of control Vol. 24; no. 2; pp. 942 - 955
• Main Authors: Zare, Kazem, Shasadeghi, Mokhtar, Izadian, Afshin, Niknam, Taher, Asemani, Mohammad Hassan
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc 01.03.2022
• Subjects: Circle criterion; Control systems design; Controllers; Fuzzy control; MIMO system; Modelling; Nonlinear control; Nonlinear systems; non‐differentiable nonlinear dynamics; quadruple tank process; Sliding mode control; switching TS fuzzy system model
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.2530

This paper presents a new approach in modeling and control of multi‐input multi‐output (MIMO) systems that have non‐differentiable operating points. A circle criterion is introduced at the non‐differentiable operating points to divide the entire operating region into two parts. Takagi‐Sugeno fuzzy models are developed in each part, and a switching framework is introduced to model the operating region. Accordingly, a sliding mode controller (SMC) is developed. The proposed modeling and controller are implemented on the benchmark quadruple tank process (QTP). It is demonstrated that the proposed modeling and controller design provides simplicity and universality in a set of nonlinear systems; it is robust with respect to various internal and external disturbances and model uncertainties which allows for accurate regulation and tracking; and it converges in finite time, is capable of controlling nonlinear systems with coupling dynamic, and enables fuzzy modeling of continuous‐time systems without imposing differentiability.