Sparse and Decoupling Control Strategies Based on Takagi-Sugeno Fuzzy Models

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear System Analysis

Background:

• Controlling multiple-input multiple-output (MIMO) systems presents challenges due to inherent coupling effects.
• Existing decentralized control structures may not efficiently handle these complex interactions.
• Accurate modeling of MIMO systems, especially nonlinear ones, is crucial for effective control design.

Purpose of the Study:

• To propose novel sparse and decoupling control strategies for MIMO systems.
• To develop computationally efficient methods for building effective Takagi-Sugeno (T-S) fuzzy models (ETSM) that accurately represent MIMO coupling effects.
• To enable the transformation of complex MIMO controller design into simpler single-input single-output (SISO) controller designs.

Main Methods:

• Utilized Type-1 and Type-2 Takagi-Sugeno (T-S) fuzzy models to represent MIMO systems.
• Employed a relative normalized gain array-based criterion to quantify coupling effects.
• Developed an effective T-S fuzzy model (ETSM) construction method for accurate coupling representation.
• Defined four indexes to extend decentralized control to a sparse control structure.
• Designed a novel ETSM-based decoupling compensator to address steady and dynamic coupling.

Main Results:

• Achieved a computationally less expensive method for building fuzzy models for MIMO systems.
• Successfully developed a sparse control strategy enabling independent SISO control loop design.
• Introduced an effective ETSM-based decoupling compensator mitigating coupling effects.
• Demonstrated that MIMO controller design can be simplified to multiple non-interacting SISO controller designs.
• Validated the proposed strategies using two illustrative examples.

Conclusions:

• The proposed sparse and decoupling control strategies effectively manage coupling effects in MIMO systems.
• These strategies allow the application of linear SISO control algorithms to nonlinear MIMO systems without requiring exact mathematical models.
• The developed ETSM approach provides a more accurate and computationally efficient way to model MIMO system coupling.
• The research facilitates the design of controllers for complex MIMO systems by breaking them down into simpler SISO problems.