The accuracy of results from experiments conducted in a wave flume is significantly impacted by the persistent reflections and re-reflections of the waves from the end of the flume. An effective method to eliminate the reflected waves involves actively controlling the wave-maker to actuate its paddle displacement motion to obtain the target wave profile specifications. This paper presents a systematic approach for modelling the relationship between the paddle displacement and the elevation of the generated waves using a Linear Time Invariant (LTI) approximation and controlling the system based on the developed model. The proposed modeling approach entails identifying an open-loop system model using input paddle displacement and the measured free surface elevation from real-time experiments. The developed model is subsequently used to design a controller based on the Internal Model Control (IMC) method. The goal is to correct the actual paddle displacement motion, eliminate reflections, compensate for the time delays, and maintain steady tracking of the target wave elevations.. The algorithm was validated in a glass flume facility, and the results from the experiments revealed that the Root Mean Square Error (RMSE) between the target wave elevation and the measured elevation of the generated waves decreased by 42 % to 56 % during the closed loop operation of the system with this controller.
Marine structures and equipment must be tested to analyze them under controlled conditions before being put to use in the real ocean. Small-scale experiments in wave flumes provide a reliable means to study the performance of such structures and equipments. These experiments involve generating water waves through the motion of wave paddles. These waves propagate towards the end of the flume and get reflected persistently towards the generating side, thus interfering with the incident waves from the wave-maker end, thereby significantly impacting the accuracy of the experimental results. To overcome this challenge, active absorption of the waves is commonly used in wave-generating facilities. The most recent effective approach for eliminating the reflective waves is the use of absorbing wavemakers with controlled paddle motion to generate the desired incident waves and absorb reflected waves at the same time. A wave elevation gauge was used as a hydraulic feedback by Milgram (1970), wherein an absorption system was built for a flap-type wavemaker. A piston-type wave absorbing system with the wave gauge mounted on the front of the wavemaker was developed by Hirakuchi et al(1990). A complex wave absorption system was designed by considering the effects of evanescent waves. An active absorption system using digital filters to estimate the active absorption transfer function was devised by Fridgaard (1995) wherein they used two wave probes and developed an active absorption system. Similar approach was followed by Schaffer (2003) wherein an absorption transfer function was developed using digital filters for non-linear wave generation case but the methodology of fitting the absorption transfer function was not adequately discussed. An active absorption system for a piston type wavemaker to compensate for the delays in the system was developed by Yang et al(2015). Subsequently, another active absorption scheme was suggested using iterative reweighted least-squares algorithm by Yang et al(2016) for approximating the absorption transfer function wherein the performance of the designed system was evaluated for both regular and irregular waves. Apart from using digital filters to design an absorption transfer function, significant efforts have been made in the recent past to develop active absorption scheme using feedback and feedforward control scheme.A self adaptive control scheme was designed by Chatry et al(1998) which was however difficult to implement in real time. Similar approaches using feedback and feedforward schemes were also reported by Bullock(1989) and De Mello et al(2013) however the control scheme was not very well articulated by the latter. A recent approach by Mahjouri et al(2020) has reported an active absorption system using real time control system without the use of feedback and feedforward loops with constant gains.