Control of Nonlinear Beam Vibrations by Multiple Piezoelectric Layers

Description

In the first part of this contribution the mechanical model of the piezoelectric beam with multiple layers is derived. Since some results of the control loop design by differential geometric methods are restricted to ordinary differential equations, the partial differential equation of the beam is approximated by a finite set of ordinary differential equations following Galerkin's method. No damping is assumed, therefore the mechanical model is a hamiltonian one. The approximating equations are of a special type, called Hamiltonian AI-systems. The second part of this contribution presents the design of the controller. After a short introduction to Hamiltonian AI-systems, the main results of the input output linearization for this special type are summarized. In contrast to general AI-systems only the knowledge of Poisson bracket is needed to do all calculations and the stability test is based on the Hamiltonian function only. Finally numerical simulations show the excellent behavior of the controlled beam.

Period	21 Apr 1997
Event title	IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems
Event type	Conference
Location	NetherlandsShow on map