Active protection of domains of a vibrating structure by using optimal control theory: A model determination

Abstract

The problem of active protection of continuous structure domains is developed by using the well known results of optimal control theory. A mathematical model of the mechanical system is defined and a spatial approximation process is presented according to the basis theory of functional analysis applied to the discretization problem. In finite dimension spaces, the state analysis is developed, including the models of the structure and the perturbation sources, and the corresponding state equations are presented. Various protection criteria compatible with the state analysis scheme are proposed and after presentation of the observer problem, the solution of the optimal regulator problem is developed. Numerical results simulating the time response of a simply supported beam under control are presented for two different protection criteria. The results allow one to proceed to a qualitative comparison of the relative merits of the chosen criteria.