Adaptive fuzzy sliding mode controller for linear systems with mismatched time-varying uncertainties

Area of Science:

• Control Systems Engineering
• Fuzzy Logic
• Nonlinear Control Theory

Background:

• Linear systems often face challenges with mismatched time-varying uncertainties.
• Traditional sliding mode control (SMC) can suffer from chattering and requires knowledge of uncertainty bounds.
• Adaptive fuzzy control offers a promising approach to handle uncertainties and improve system performance.

Purpose of the Study:

• To present a new design for an adaptive fuzzy sliding mode controller (AFSMC) for linear systems with mismatched time-varying uncertainties.
• To develop a controller that guarantees stability and robustness without prior knowledge of uncertainty bounds.
• To reduce the chattering phenomenon inherent in conventional sliding mode control.

Main Methods:

• Designing a sliding function coefficient matrix to satisfy a sliding coefficient matching condition for bounded uncertainties.
• Proposing an AFSMC that utilizes on-line adaptation of fuzzy set parameters to enhance control performance.
• Employing a fuzzy mechanism to adapt controller parameters in real-time.

Main Results:

• The proposed AFSMC design ensures system stability and invariance on the sliding surface.
• The controller effectively handles time-varying uncertainties without requiring their bounds to be known in advance.
• Simulation results demonstrate the effectiveness of the AFSMC in improving control performance and reducing chattering.

Conclusions:

• The developed AFSMC provides a robust and effective solution for controlling linear systems with uncertainties.
• The on-line adaptation mechanism significantly improves the performance of the fuzzy sliding mode control system.
• The AFSMC approach offers a practical method for mitigating chattering in sliding mode control applications.