Boundary Control Approach to the Spectral Estimation Problem: The Case of Simple Poles

2009 ◽  
Vol 8 (3) ◽  
pp. 225-248
Author(s):  
Sergei Avdonin ◽  
Anna Bulanova ◽  
Dmitry Nicolsky
Keyword(s):  
Boundary Control ◽  
Spectral Estimation ◽  
Estimation Problem ◽  
Control Approach

Active Boundary Control of Elastic Cables

1995 ◽  
Author(s):  
Catalin F. Baicu ◽  
Christopher D. Rahn
Keyword(s):  
Boundary Control ◽  
Nonlinear Partial Differential Equations ◽  
Lyapunov Theory ◽  
Structural Elements ◽  
Control Approach ◽  
Out Of Plane ◽  
Boundary Force ◽  
Active Vibration ◽  
Natural Boundary Conditions ◽  
Modal Dynamics

Abstract Cables are lightweight structural elements used in a variety of engineering applications. This paper introduces an active boundary control approach that damps undesirable vibrations in a cable. Using Hamilton’s principle, the governing nonlinear partial differential equations for an elastic cable are derived, including the natural boundary conditions associated with boundary force control. Based on Lyapunov theory, passive and active vibration controllers are developed. A Galerkin approach generates the linearized, closed loop, modal dynamics equations for out-of-plane vibration. Simulations demonstrate the improved damping provided by the passive and active controllers.

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