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 incoming vibrational power to be selectively absorbed. Matched termination, non-causal, causal fixed-form and Wiener-Hopf feedback solutions are derived. These solutions, including a positive real approximation to the Wiener-Hopf solution, are illustrated through an extensive example for the free end of a dispersive Bernoulli-Euler beam. Several interesting results arise from this research. A matched termination, absorbing all impinging energy, is a subset of the optimal, non-causal solution. As a result, performance ranging from that achieved with simple rate feedback to that exceeding the matched termination is possible with increasingly complex configurations of control hardware. In the formulation of the control, information about the spectral content of the incoming waves can be used to frequency-tailor the control performance. The wave mode control formulation reveals that performance can be improved by using more than one distinct actuator and sensor at the active junction, a process not generally practiced in structural control. Finally, given the appropriate control hardware and particular structural geometries, optimal wave control can be used to eliminate resonant behavior or dynamically isolate one structural region from another. © 1990.