Unknown Input Observer Design for Interval Type-2 T-S Fuzzy Systems With Immeasurable Premise Variables

Area of Science:

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

Background:

• Designing fault detection observers for nonlinear systems with immeasurable states is challenging.
• Interval type-2 Takagi-Sugeno (T-S) fuzzy systems offer enhanced modeling capabilities for nonlinear dynamics.
• Systems often experience immeasurable premise variables, time-varying delays, and unknown inputs, complicating observer design.

Purpose of the Study:

• To develop robust unknown input fault detection observers (UIFDOs) for interval type-2 T-S fuzzy systems.
• To address the challenges posed by immeasurable premise variables, time-varying delays, and unknown inputs.
• To ensure observer residuals are sensitive to faults while robust to exogenous signals.

Main Methods:

• The design procedure considers both measurable and immeasurable premise variables.
• Sufficient design conditions are derived using linear matrix inequalities (LMIs).
• The proposed UIFDO is evaluated for its effectiveness in fault detection and robustness.

Main Results:

• The proposed method successfully designs stable observers for interval type-2 T-S fuzzy systems with immeasurable premise variables.
• The effectiveness of the UIFDO is demonstrated through simulations on a numerical example, detecting two distinct fault types.
• A comparison highlights the superiority of interval type-2 T-S fuzzy models over type-1 for fault detection.

Conclusions:

• The developed UIFDO provides a robust solution for fault detection in complex nonlinear systems.
• The method is applicable to systems with immeasurable premise variables and time-varying delays.
• The study validates the enhanced performance of interval type-2 fuzzy systems in fault detection applications, as shown with a one-link manipulator example.