Improvement of an Algebraic Observer for the Control of a One-Story Building

Abstract

This article presents an improvement to an algebraic observer to estimate the state of a mechanical system whose only feedback variable is acceleration. This problem appears in different mechanical systems, e.g., structures subject to the effects of earthquakes. The algebraic observer that motivates this work is constrained to a finite time range; it cannot observe for time very close to zero, nor beyond a large value, because it would make singular the matrix involved in the estimation. In this proposal these disadvantages are eliminated by obtaining a matrix with independent-of-time determinant. The objective of the observer is to estimate the position and velocity that correspond to the acceleration measure, for use in a recently published control law of the semi-active control system of a single-story building by means of a magnetorheological damper.