A natural observer for optimal state estimation in second order linear structural systems

A state observer for mechanical and structural systems is derived in the context of the second order differential equation of motion of linear structural systems. The proposed observer possesses similar characteristics to the Kalman filter in the sense that it minimizes the trace of the state error covariance matrix within the predefined structure of the feedback gain. The main contribution of the paper consists of the fact that the proposed observer can be implemented directly as a modified linear finite element model of the system, subject to collocated corrective forces proportional to the measured response. The proposed algorithm is effectively illustrated in two different types of second order systems; a close-coupled spring–mass–damper multi-degree of freedom system and a plate subject to transverse vibrations.

► A natural state observer for linear second order systems is presented.
► The proposed observer minimizes the state error covariance given the structure of the feedback gain.
► The proposed state observer can be implemented directly as a modified finite element model of the system.
► The proposed state observer can account directly for colored excitation without state augmentation.