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

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.