An iterative re-weighted least-squares algorithm for the design of active absorbing wavemaker controller

In physical model tests for highly reflective structures, one often encounters a problem of multiple reflections between the reflective structures and the wavemaker. Absorbing wavemakers can cancel the re-reflective waves by adjusting the paddle motion. In this paper, we propose a method to design the controller of the 2-D absorbing wavemaker system in the wave flume. Based on the first-order wavemaker theory, a frequency domain absorption transfer function is derived. Its time realization can be obtained by designing an infinite impulse response(IIR) digital filter, which is expected to approximate the absorption transfer function in the leastsquares sense. A commonly used approach to determine the parameters of the IIR filter is applying the Taylor expansion to linearize the filter formulation and solving the linear least-squares problem. However, the result is not optimal because the linearization changes the original objective function. To improve the approximation performance, we propose an iterative reweighted least-squares(IRLS) algorithm and demonstrate that with the filters designed by this algorithm, the approximation errors can be reduced. Physical experiments are carried out with the designed controller. The results show that the system performs well for both regular and irregular waves.