Observability and State Estimation for Smooth and Nonsmooth Differential Algebraic Equation Systems

TL;DR

This paper extends observability analysis and state estimation techniques to smooth and nonsmooth DAE systems, introducing a new test and an extended Kalman filter, demonstrated on a wind turbine model.

Contribution

It introduces the lexicographic SERC observability test and a sensitivity-based extended Kalman filter for DAE systems, including nonsmooth cases.

Findings

The L-SERC test effectively determines observability in DAE systems.

The S-EKF accurately estimates states in both smooth and nonsmooth DAE models.

Application to wind turbine system validates the proposed methods.

Abstract

In this work, we extend the sensitivity-based rank condition (SERC) test for local observability to another class of systems, namely smooth and nonsmooth differential-algebraic equation (DAE) systems of index-1. The newly introduced test for DAEs, which we call the lexicographic SERC (L-SERC) observability test, utilizes the theory of lexicographic differentiation to compute sensitivity information. Moreover, the newly introduced L-SERC observability test is useful in the context of partial observability as it can judge which states are observable and which are not. Additionally, we introduce a novel sensitivity-based extended Kalman filter (S-EKF) algorithm for state estimation, applicable to both smooth and nonsmooth DAE systems. Finally, we apply the newly developed S-EKF to estimate the states of a wind turbine power system model.