Hybrid compensation control for affine TSK fuzzy control systems

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear Control Theory

Background:

• Designing state feedback controllers for affine Takagi-Sugeno-Kang (TSK) fuzzy models presents challenges in ensuring stability and performance, especially when fuzzy rules vary widely.
• Existing robust control approaches that treat rule variations collectively can lead to unsatisfied stability conditions and unpredictable closed-loop system performance.

Purpose of the Study:

• To propose a new state feedback controller design methodology for affine TSK fuzzy models.
• To develop a controller that compensates for all fuzzy rules individually to achieve desired overall system performance.
• To overcome limitations of previous approaches that may fail to satisfy stability conditions for widely distributed fuzzy rules.

Main Methods:

• Combining two distinct control design methodologies to create a novel controller.
• Treating each fuzzy rule as a variation of a nominal rule.
• Individually analyzing and compensating for rule variations using a Lyapunov stability approach.

Main Results:

• The proposed controller design effectively compensates for all fuzzy rules, ensuring desired control performance.
• The individual treatment of rule variations in a Lyapunov sense enhances stability conditions, even with wide rule distribution.
• Demonstrated effectiveness through various simulation examples, illustrating good control performances.

Conclusions:

• The proposed method offers a more predictable and stable approach to designing state feedback controllers for TSK fuzzy models compared to robust control methods.
• This approach ensures that desired control performance is achieved across the entire operating range of the fuzzy system.
• The individual compensation strategy is crucial for maintaining stability and performance when dealing with significant variations in fuzzy rules.