Prescribed-Time Fault Estimation and Unknown Input Compensation by Using Periodic Delayed Approach

Area of Science:

• Control Systems Engineering
• Fault Detection and Diagnosis
• Linear System Analysis

Background:

• Sensor faults and unknown inputs pose significant challenges in linear control systems.
• Existing fault estimation methods often lack precise timing guarantees.
• Prescribed-time stability offers enhanced control over system convergence.

Purpose of the Study:

• To design prescribed-time sensor fault estimators (PSFEs) for linear systems.
• To develop controllers for unknown input compensation achieving prescribed-time stability.
• To address limitations of differentiability in fault estimation.

Main Methods:

• A novel filter is introduced to handle non-differentiable sensor faults.
• The problem is transformed into designing prescribed-time unknown input observers for augmented systems.
• Generalized inverse and periodic delayed outputs are utilized for observer and controller design.
• Both full-and reduced-order PSFEs are developed.

Main Results:

• Effective PSFEs are designed, capable of estimating sensor faults within a prescribed time.
• Periodic delayed controllers are successfully designed for unknown input compensation.
• The closed-loop system is demonstrated to be T-prescribed-time stable (T-PS).

Conclusions:

• The proposed methods provide a robust framework for fault estimation and control in linear systems with precise timing.
• The approach effectively compensates for unknown inputs and ensures prescribed-time stability.
• The efficacy of the developed techniques is validated through a practical example.