Extended State Observer for Mismatch Disturbances Using Taylor Approximation of the Integral

TL;DR

This paper presents a novel extended state observer method that uses Taylor approximation to estimate disturbances in initially unobservable systems, ensuring exponential stability and robustness.

Contribution

It introduces a new approach combining Taylor expansion with ESOs to handle unobservable systems for disturbance estimation.

Findings

Achieves exponential stability of the observer error dynamics.

Demonstrates effectiveness through a practical example.

Enhances disturbance estimation robustness in unobservable systems.

Abstract

The development of disturbance estimators using extended state observers (ESOs) typically assumes that the system is observable. This paper introduces an improved method for systems that are initially unobservable, leveraging Taylor expansion to approximate the integral of disturbance dynamics. A new extended system is formulated based on this approximation, enabling the design of an observer that achieves exponential stability of the error dynamics. The proposed method's efficacy is demonstrated through a practical example, highlighting its potential for robust disturbance estimation in dynamic systems.