A New Fuzzy PID Control System Based on Fuzzy PID Controller and Fuzzy Control Process
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A New Fuzzy PID Control System Based on Fuzzy PID Controller and Fuzzy Control Process Nguyen Dinh Phu1 • Nguyen Nhut Hung1 • Ali Ahmadian2
•
Norazak Senu3
Received: 17 February 2020 / Revised: 11 May 2020 / Accepted: 10 June 2020 Ó Taiwan Fuzzy Systems Association 2020
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
& Ali Ahmadian [email protected] Nguyen Dinh Phu [email protected] Nguyen Nhut Hung [email protected] 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
1 Introduction 1.1 Background information The applications of the fuzzy theory to knowledge-based systems in process control are grown (can see in [7, 26]). Especially, in fuzzy control theory, there were some studies related to the concept of fuzzy PID controllers. For example, Zhao et al. [27] proposed a fuzzy gain scheduling scheme of PID controllers for process control in 1993. This scheme applies fuzzy rules and reasoning to determine the controller parameters based on the error signal and its first difference, then the PID controller generates the control signal. Mizumoto [18] showed that PID controllers can be realized by fuzzy control methods called ‘‘product-sumgravity method’’ and ‘‘simplified fuzzy reasoning method’’. Therefore, PID controls are shown to be a special case of fuzzy controls. Most recently, Zhao et al. [28] presented a general type-2 fuzzy gain scheduling PID controller to achieve self-balance adjustment of the power-line inspection robot system. Tsai et al. [13] proposed a new adaptive PID control method using predictive control and output recurrent fuzzy wavelet neural network for a group of nonlinear digital time-delay dynamic systems. Lv et al. [17] investigated a stochastic stabilization problem of uncertain networked control systems involving Takagi– Sugeno (T-S) fuzzy model, transmission delays and external disturbances. They combined a T-S fuzzy model with a fuzzy PID controller and modeled uncertain networked control systems with random communication delays and external disturbances. Then, these systems were simplified through a mathematical method, and the stabi
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