Algebraic PI observer for velocity and displacement in civil structures from acceleration measurement

Abstract

This study aims to deal with the velocity and displacement estimation problem in civil structures through acceleration measurements. Nowadays, different schemes have been proposed to solve this problem, however, most proposed observer schemes generally require the Luenberger structure and sometimes any base transformation. In contrast, this paper provides a novel algebraic Proportional Integral (PI) observer based on the Algebraic Observability Condition (AOC), which allows the representation of the velocity and displacement terms as a function of the acceleration measurements, does not need a coordinate transformation, and uses proportional and integral correction of the estimation error. Moreover, a simple criterion for the observer gains selection is provided in order to ensure asymptotic convergence which leads to the fact that the gains can be assigned without using any numerical method to calculate them. An advantage of this observer is that it can be easily implemented for practical purposes. Finally, the effectiveness and accuracy of this estimation method are demonstrated experimentally via a reduced-scale five-story building prototype.