Fuzzy modeling with multivariate membership functions: gray-box identification and control design

Area of Science:

• Engineering
• Control Systems
• Fuzzy Logic

Background:

• Fuzzy modeling and model-based control are crucial for complex systems.
• Takagi-Sugeno (TS) models offer a structured approach to fuzzy modeling.
• Efficient parameter estimation and control design are key challenges.

Purpose of the Study:

• To introduce a novel framework for fuzzy modeling and model-based control design.
• To develop methods for estimating TS fuzzy model parameters using constrained optimization.
• To create techniques for control design via model linearization and inversion.

Main Methods:

• Utilized Takagi-Sugeno (TS) type fuzzy models with constant consequents.
• Employed multivariate antecedent membership functions derived from Delaunay triangulation.
• Implemented an iterative insertion algorithm for characteristic point determination.
• Applied constrained optimization for parameter estimation, incorporating a priori process knowledge.
• Developed control design strategies through model linearization and inversion.

Main Results:

• Successfully identified the Box-Jenkins gas furnace model using the proposed framework.
• Demonstrated inverse model-based control for a pH process.
• Achieved comparable or improved results against existing literature benchmarks.
• Validated the effectiveness of the novel fuzzy modeling and control design techniques.

Conclusions:

• The proposed framework provides an effective approach for fuzzy modeling and model-based control design.
• The integration of Delaunay triangulation and constrained optimization enhances model accuracy and control performance.
• The demonstrated applications highlight the versatility and efficacy of the developed methods.