Abstract
This paper analyzes the stability of fuzzy control systems with applications for electric drives. Ensuring the stability of these systems is a necessity in practice. The purpose of the study is the analysis of the dynamic characteristics of the speed control systems of electric drives based on fuzzy PI controllers in the context of performing stability analyses, both internal and input–output, finding solutions to stabilize these systems and provide guidance on fuzzy regulator design. The main methods of treatment applied are as follows: framing the control system in the theory of stability of multivariable non-linear systems, application of Lyapunov’s theory, performing an input–output stability analysis, and verification of the stability domain. The article presents the conditions for correcting the fuzzy controller to ensure internal and external stability, determines the limits of the stability sector, and gives indications for choosing the parameters of the controller. The considerations presented can be applied to various structures for regulating the speed of electric drives which use various PI fuzzy controllers.
Highlights
IntroductionThe study presented in this paper fits into the broader context of the mathematics of fuzzy controllers, Mamdani structures, and the control of electric drives, as well as the industrial application of fuzzy control systems
There are particular cases of the use of fuzzy PI regulators. Their widespread application in commercial equipment to control electric drives is hampered by a number of impediments, such as the lack of precise methods for designing control systems based on fuzzy logic, the lack of precise methods of stability analysis, based on which one can be confident that they can undoubtedly ensure a certain quality of stability of the control systems of electric drives, and, the increased complexity of the development systems of driving equipment based on fuzzy logic
The object of the stability analysis performed in the paper was a speed regulation system of an electric drive with a direct current motor, in which a speed regulator of PI
Summary
The study presented in this paper fits into the broader context of the mathematics of fuzzy controllers, Mamdani structures, and the control of electric drives, as well as the industrial application of fuzzy control systems. Various scientific papers have appeared in the literature for many years, presenting examples of the use of fuzzy logic in regulating the speed of electric drives [1,2]. Fuzzy logic is an instrument of artificial intelligence which translates human reasoning into numerical calculations [4,5]. In these studies, there are particular cases of the use of fuzzy PI regulators. Their widespread application in commercial equipment to control electric drives is hampered by a number of impediments, such as the lack of precise methods for designing control systems based on fuzzy logic, the lack of precise methods of stability analysis, based on which one can be confident that they can undoubtedly ensure a certain quality of stability of the control systems of electric drives, and, the increased complexity of the development systems of driving equipment based on fuzzy logic
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