Authors: Nguyen Dinh Phu1 • Nguyen Nhut Hung1 • Ali Ahmadian2 • Norazak Senu3

Affiliations:

^[1] Faculty of Engineering Technology, Quang Trung University, Quy Nhon City, Vietnam

^[2] Institute of IR 4.0, The National University of Malaysia, 43600 UKM Bangi, Selangor, Malaysia

^[3] Institute for Mathematical Research (INSPEM), University Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

Received: 17 February 2020 / Revised: 11 May 2020 / Accepted: 10 June 2020

Taiwan Fuzzy Systems Association 2020

Article type: Research Article

Abstract:  In this paper, we present a fuzzy PID control system as a combination of a fuzzy PID controller and a fuzzy control process, which is represented by a fuzzy control differential equation in linear form. We use the concepts of the generalized Hukuhara differentiability and the fuzzy integral of fuzzy-valued functions to study some qualitative properties for this system in the space of fuzzy numbers. We also study the existence and uniqueness result for solutions of fuzzy PID control differential equations under some suitable conditions. A number of examples are also provided to illustrate the results of the theory.

Keywords:  Fuzzy PID controller  Generalized Hukuhara differentiability  Fuzzy differential equations  Fuzzy PID control system