This paper presents the design and implementation of a wave excitation force estimator based on the cubature Kalman filter (CKF) [1] for a CETO 6, a submerged wave energy converter (WEC) device with three PTOs.A wave (excitation force) estimator is a kind of virtual sensor which computes the force applied by the waves to a floating or submersed body, such as a WEC buoy (or a vessel), from available measurements (for WECs, usually from buoy motion and PTO force sensors).Wave excitation force estimation is required by many advanced WEC control approaches. In the model predictive control (MPC) framework [2], for instance, the wave estimator feeds a wave predictor, which in turns forecasts the future values of wave excitation force. In other control frameworks, such as the “simple-but-effective” controller in [3], it provides an estimate of the current wave excitation force to a second estimator which computes its dominant frequency (and amplitude). The literature on the design of wave estimators for WECs is relatively rich for the 1 DoF case (see [4] for a review), but quite scarce for multi-DoF devices.Paper [5], where wave excitation force estimation and prediction have been studied for a spar-buoy WEC, is probably the first published study dealing with wave estimation in 3-DoF. An extended Kalman filter approach is presented which considers the wave excitation force as a sum of time-varying sinusoids. Taken on the average, the simulation results show good estimation accuracy in the heave direction, but much less good in the surge and pitch directions. Unfortunately, the performance significantly drops for several sea states. For a WaveSub-like device, a submerged WEC with 4 PTOs, a multi-DOF extension of the “simple-but-effective” controller is developed in [6], and an MPC in [7]. The estimation results presented in [6] for the surge and heave directions look perfect, but no details on the dynamic observer are given. In [7], however, the authors say that they use a 3–DoF extension of the Kalman Filter approach proposed in [8]. This time, the plots show some mismatch between estimated wave and “true” excitation force in surge and heave directions. No results are given for the pitch direction, nor for off-axis loading cases that would excite other directions, too.The advantages of CKF wave estimator described in the paper are its performance and ease of tuning when working with high-order systems. A linear state-space model of order 66 with 9 inputs and 6 outputs is used to “guess” the system dynamics at the cubature points in order to perform the time update and the measurement update steps. Preliminary results are presented both for nominal conditions and for mismatch conditions, where the estimator is applied to a full nonlinear model of the system.[1] I. Arasaratnam and S. Haykin. “Cubature kalman filters”. In: IEEE Transactions on automatic control 54.6 (2009).[2] H.-N. Nguyen et al,. “Experimental validation of a nonlinear MPC strategy for a wave energy converter prototype". In Proc. of the 35th OMAE Conference, Busan, Republic of Korea (2016).&nbsp;[3] F. Fusco and J.V. Ringwood. “A Simple and Effective Real-Time Controller for Wave Energy Converters”.In: Sustainable Energy, IEEE Transactions on 4.1 (2013).[4] Y. Peña-Sanchez et al., “A Critical Comparison of Excitation Force Estimators for Wave-Energy Devices”. In: IEEE Transactions on Control Systems Technology (2019)[5] B. A Ling. “Real-time estimation and prediction of wave excitation forces for wave energy control applications”. MA thesis. Oregon State University, (2015).[6] A. J. Hillis et al., “Power capture gains for the WaveSub submerged WEC using active control”. In: Proceedings of the 13th EWTEC Conference, Naples, Italy (2019).[7] A.J. Hillis et al., “Model predictive control of a multi-degree-of-freedom wave energy converter with model mismatch and prediction errors”. In: Ocean Engineering 212 (2020).[8] H.-N. Nguyen and P. Tona. “Wave excitation force estimation for wave energy converters of the point absorber type”. In: IEEE Transactions on Control System Technology (2018).

Wave Excitation Force Estimation for a Multi-Dof Wec via a Cubature Kalman Filter: Design and Preliminary Results

Paper Proceedings: https://asmedigitalcollection.asme.org/OMAE/OMAE2021/volume/85116

OMAE 2021

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