A General Model-Based Extended State Observer with Built-In Zero Dynamics

TL;DR

This paper introduces a general model-based extended state observer (GMB-ESO) for linear systems, establishing conditions for its existence, analyzing its convergence, and proposing an improved version with built-in zero dynamics for systems with zero dynamics.

Contribution

The paper presents the first conditions for GMB-ESO existence, analyzes its error characteristics, and introduces an improved GMB-ESO with built-in zero dynamics for complex systems.

Findings

GMB-ESO exists if the plant is observable and has no invariant zero.

GMB-ESO converges finitely and matches UIO in disturbance estimation under certain conditions.

An improved GMB-ESO with built-in zero dynamics is proposed for plants with zero dynamics.

Abstract

A general model-based extended state observer (GMB-ESO) is proposed for single-input single-output linear time-invariant systems with a given state space model, where the total disturbance, a lump sum of model uncertainties and external disturbances, is defined as an extended state in the same manner as in the original formulation of ESO. The conditions for the existence of such an observer, however, are shown for the first time as 1) the original plant is observable; and 2) there is no invariant zero between the plant output and the total disturbance. Then, the finite-step convergence and error characteristics of GMB-ESO are shown by exploiting its inherent connection to the well-known unknown input observer (UIO). Furthermore, it is shown that, with the relative degree of the plant greater than one and the observer eigenvalues all placed at the origin, GMB-ESO produces the identical disturbance estimation as that of UIO. Finally, an improved GMB-ESO with built-in zero dynamics is proposed for those plants with zero dynamics, which is a problem that has not been addressed in all existing ESO designs.