A new approach to the modeling of distributed structures for control

Building structures represent complex distributed-parameter systems. The motion of such systems is described by partial differential equations complemented by suitable boundary conditions. For control design purposes, distributed-parameter systems must be discretized in the spatial variables. But, if the discrete model is not sufficiently accurate, controls designed on the basis of the discrete model can destabilize the actual distributed structure, in which case the controls are said to be sensitive to discretization errors. This paper presents a new approach to the discretization of distributed structures yielding accurate discrete models of relatively low order. A numerical example illustrates how controls can be designed for a complex structure subjected to earthquake excitations.