Gain-phase margin analysis of dynamic fuzzy control systems.

Area of Science:

• Control Engineering
• Nonlinear Systems Analysis
• Fuzzy Logic Systems

Background:

• Fuzzy control systems are widely used but often exhibit nonlinear behavior, making stability analysis challenging.
• Predicting limit cycles is crucial for understanding system robustness and performance.
• Existing methods may not fully address the complexities of dynamic fuzzy control systems with adjustable parameters.

Purpose of the Study:

• To develop and apply effective methods for predicting limit cycles in dynamic fuzzy control systems.
• To analyze the stability and robustness of both continuous-time and sampled-data fuzzy control systems.
• To propose a method for determining gain and phase margins related to limit cycle occurrence.

Main Methods:

• Application of the gain-phase margin tester.
• Utilizing the describing function method for linearization of fuzzy controllers.
• Employing parameter plane analysis for stability investigation.
• Extension of methods to both continuous-time and sampled-data systems.

Main Results:

• Demonstrated prediction of limit cycles in dynamic fuzzy control systems.
• Successfully analyzed stability of equivalent linearized systems with adjustable parameters.
• Presented a straightforward approach to determine critical gain and phase margins for robustness.
• Validated the methods through examples of continuous-time and sampled-data fuzzy control systems.

Conclusions:

• The applied methods provide effective tools for predicting limit cycles in dynamic fuzzy control systems.
• The proposed approach enhances the understanding of stability and robustness in these systems.
• The techniques are applicable to both continuous-time and sampled-data fuzzy control configurations.