Robustness Issues in Boundary Feedback of Flexible Structures

Transfer function models for basic structural elements with boundary control reveal certain inherent properties relevant to questions of control system realization, design, and analysis of robustness. The transfer functions involved are not strictly proper, may be nonminimum phase (except for the special case of colocated actuation and sensing), and often have large number of poles on the imaginary axis. In this paper we consider these basic questions in terms of modeling and control system design for robustness. We investigate the application of algebraic methods for computing stabilizing control based on certain exact, irrational transfer functions. We consider boundary control of the wave equation and suggest extension of the method to more general problems. Special attention is given to implementation issues associated with a class of infinite dimensional control laws of the type described by Baras.