On observability analysis and observer design for a class of nonlinear uncertain systems with general elastic vibration dynamics

Abstract

This paper focuses on the observability analysis for a general class of rigid-flexible coupling systems constituted of rigid-body mode and elastic vibration modes with uncertain dynamics and disturbances. And the measured output is a linear combination of rigid-body mode and elastic vibration modes.Firstly, the necessary and sufficient condition of the observability for such system is given. Secondly, the general extended state observer design is proposed to estimate the states of both rigid-body mode and elastic vibration modes as well as "total disturbance." Next, the convergence of estimation errors of the general extended state observer is discussed. Then, under unobservable case, a compressed extended state observer is designed to estimate the states and the "total disturbance" acting on rigid-body mode, and the corresponding estimation errors are studied. In addition, the theoretical results are demonstrated via the simulation on a rigid-flexible coupling system.

Estimation of wheel–rail structural interactions from motion signals of high-speed train bogie

“…Hence, when the ESO system is observable and h is bounded, the estimation error xe (t) will be bounded. The upper bound of the estimation error can be readily obtained when the observer poles are selected [22].…”

“…The observability condition of the ESO for large-scale systems has been studied before. In [22] and [31], the observability condition of the ESO is found to be m ≥ q. We have derived the observability condition using the block matrix properties and proposed a different way to check the rank of the matrix O λ .…”

“…The observability of the ESO has drawn much attention from researchers when dealing with large-scale systems. The sufficient condition for observability of the ESO for structural systems with rigid body and elastic modes has been found in [22]. To investigate the observability of the ESO for reconstructed extended observer system, the special structure of the ESO helps us find the minimum number of sensors to estimate the wheel-rail dynamics, which has not been studied in other publications to the best of author's knowledge.…”

Optimal resource allocation for high‐order nonlinear uncertain multi‐agent systems

“…Since the disturbance or uncertainty is estimated and compensated before it brings negative influence on control systems, this disturbance estimation and compensation method possesses the merit of actively rejecting the disturbance, leading to the name of ADRC. The preliminary idea of ADRC was proposed in 1980s, 31 and has been investigated in depth in References 33‐38. The ADRC has been successfully applied to a broad class of practical control systems 39‐42 …”