Analytical Implementation of Wave-Absorbing Control for Flexible Beams Using Synchronization Condition

Abstract

For wave-absorbing control, the ideal controller transfer function H(s), which connects the sensor output to the control force, contains the imaginary unit i = −1 explicitly. Therefore, H(s) cannot be implemented directly by convolution integration of the sensor output with the inverse Laplace transform of H(s). In this paper, this problem is solved by imposing the synchronization condition on the bases of H(s). The condition requires that the instantaneous frequencies of the control force and the incident wave be the same. In other words, the instantaneous frequency of the control force varies with time in synchronization with the frequency components of the wave that are arriving at the wave-absorbing point with different group velocities. Therefore, the condition is referred to as the synchronization condition in this paper. The solution method is applicable to various combinations of sensor and actuator. Experimental verification is presented for a simulated case. The parameters of the digital algorithm for the experiment are determined analytically by using a complex error function and a generating function expansion of the Bessel function.