Ultimate Boundedness of the Response of a Drilling Pipe Model

The drill pipe model described by the wave equation with boundary conditions is reduced through the d'Alembert transformation to a difference equation model and an ultimate bound for the velocity at the bottom of the pipe is obtained. The proposal of an energy function for the distributed model allows to provide an ultimate bound for a measure of the distributed variables describing the system in terms of LMI conditions. The two approaches are compared through an ilustrative example.