A Backstepping Boundary Observer for a Simply Supported Beam

This paper presents the development of a full-state observer for an Euler-Bernoulli beam system with simply supported boundary conditions. This problem is motivated by the necessity of estimators in control and diagnostic applications. The observer is developed using a backstepping procedure. The full state observer cannot be completed with a single observer system, and hence this paper presents the synthesis of two observer structures that together provide the desired convergence. The necessary feedback information is limited to the slope and the sheer force of the beam at one boundary, which are practically measurable values on a physical system. The observer estimates the full infinite dimensional beam system without any discretization of the model. The result of the technique developed in this paper is that the infinite dimensional observer estimates converge to the plant system states (representing the actual beam displacement) at an arbitrary exponential rate; numerical simulation results validating this behavior are provided.