Optimal Control of Power Flow at Structural Junctions

This paper describes several techniques for deriving optimal feedback compensators for structural waveguides at junctions. A frequency dependent cost functional composed of power flow and control effort, is minimized. Control of power flow, by modifying junction reflection and transmission properties, enables selective absorption of incoming vibrational power. Noncausal, causal fixed-form and Weiner-Hopf feedback solutions are derived. These solutions, including a positive real approximation to the Weiner-Hopf solution, are illustrated through an extensive example for the free end of a dispersive Bernoulli-Euler beam.