Abstract
Travelling wave generation in finite structures is an engaging topic that has given rise to various research opportunities. A number of feed-forward techniques including two mode excitation, impedance matching and active sink have been developed to generate travelling waves in solids. Although these techniques have shown to be adequate in laboratory settings, especially for long, slender beams, they require laborious tuning procedures which do not guarantee desired trajectories and are followed in light of interference from noise and unwanted perturbations. By all account, a robust travelling wave device is one that can handle unwanted perturbations and noise in real time using feedback control. A closed loop back-stepping control method attenuated with two mode excitation is utilised to generate desired travelling waves on a finite structure. The method utilises piezoelectric patches for actuation and sensing. The orthogonality of the longitudinal modes is exploited to decompose the modal vibrations of two consecutive modes. The modal vibrations are then regulated using an feedback control scheme such that the two consecutive modes have the same amplitude and a phase difference of 90°, which is a required condition to obtain a travelling wave in finite structures. A parameter estimation method using orthogonal decomposition is utilised to calculate the modal amplitude from the beam displacement and also to calculate the excitation forces required to regulate the modal amplitude of two consecutive modes. The closed loop method is implemented on a fixed-fixed Euler Bernoulli beam model to verify the feedback control strategy and test the modal estimation method.
