Guidance of a moving sensor used in state estimation of a flexible beam

In certain applications involving structural systems, the use of multiple high end sensors may prove to be prohibitive. The alternative would be to use fewer, or even a single sensing device that is capable of moving across the span of the structural system. In this work, a one dimensional flexible beam, described by an Euler-Bernoulli partial differential equation is considered. It is assumed that a velocity sensor obtaining pointwise (in space) velocity measurements is capable of moving across the beam. A Luenberger observer whose filter gain is expressed as a function of the moving sensor location is proposed. Using Lyapunov redesign methods, similar to those employed in adaptive systems, the guidance of the moving sensor is obtained and which solely depends on the state estimation error at the current sensor position. The guidance policy is performance-based and steers the sensor to spatial regions with larger estimation errors. Extensions of the proposed guidance laws take into account the motion dynamics of a mobile sensor. Extensive numerical studies examine the feasibility of a mobile sensor used for the improved state estimation of a flexible beam.