1 Observer-Based Unknown Input Estimator of Wave Excitation Force for a Wave Energy Converter Mustafa Abdelrahman and Ron Patton, Life Fellow, IEEE Abstract—Several energy maximization control approaches for Point Absorber Wave Energy Converter (PAWEC) systems re- 2 quire knowledge of the Wave Excitation Force (WEF) which is not measurable during PAWEC operation. Many WEF estimators 4 have been proposed based on stochastic PAWEC modelling using the Kalman Filter (KF), Extended Kalman Filter (EKF) or 6 receding-horizon estimation. Alternatively, a deterministic WEF estimator is proposed here based on the Fast Unknown Input 8 Estimation (FUIE) concept. The WEF is estimated as an unknown input obviating the requirement to represent its dynamics. The 10 proposed Observer-Based Unknown Input Estimator (OBUIE) inherits the capability of estimating fast-changing signals from 12 the FUIE which is important when considering irregular wave conditions. Unlike preceding methods the OBUIE is designed 14 based on a PAWEC model including the nonlinear viscous drag force. It has been shown that the nonlinear viscous drag 16 force is essential for accurate PAWEC model description, within the energy maximization control role. The performance of the 18 proposed estimator is evaluated in terms of PAWEC conversion efficiency in a single degree-of-freedom PAWEC device operating 20 in regular and irregular waves. Simulation results are obtained using Matlab to evaluate the estimator under different control 22 methods and subject to parametric uncertainty. Index Terms—Wave Energy Conversion, Wave Excitation 24 Force, Point Absorber, Unknown Input Observer, Monte Carlo Methods 26 I. I NTRODUCTION W AVE energy conversion is gaining attention among 28 marine renewable energy options thanks to high energy density of ocean waves compared with the energy density 30 available from wind [1]. There is also a need for diversity in the use of renewable energy sources since most sources 32 are not available all the time. A disadvantage of wave power is the relatively high cost of energy compared with wind 34 power and is hence still not economically competitive [2], even if the potential for technology development is high. 36 Some investigators, e.g., [2], [3] and [4], have clarified the importance of using well designed estimation and automatic 38 control to achieve energy maximisation as a key link to reduce the cost of energy. Several control techniques have 40 been proposed to achieve wave energy conversion power max- imization, such as reactive, latching control, Model Predictive 42 Control (MPC) and etc., see [3]. Some methods require the Wave Excitation Force (WEF) to calculate an optimal (in the 44 sense of power maximization) control to facilitate adaptation to changing sea conditions. Some methods, e.g., MPC, even 46 require future WEF information that can be obtained via M. Abdelrahman and R. Patton are with the School of Engineering and Computer Science, The University of Hull, Cotingham Road, Hull, UK e-mail: (m.a.abdelrahman@2014.hull.ac.uk(M. Abdelrahman), r.j.patton@hull.ac.uk (R. Patton). prediction. However, WEF is not directly measurable during 48 PAWEC operation and hence it should be calculated/estimated from other available or redundant PAWEC measurements. 50 Several studies have proposed WEF estimators based on the Kalman Filter (KF) [5], [6], [7], [8] and the Extended 52 Kalman Filter (EKF) [9]. In general, good estimation of WEF is obtained using the KF-based approaches utilizing 54 measurement of PAWEC output(s) and input. However, the KF-based WEF estimators necessitate the WEF dynamics to 56 be represented in the estimator model. The WEF dynamics are usually approximated by a set of Harmonic Oscillators with 58 a range of frequencies that should be specified based on the incoming wave, which is unknown. The number of Harmonic 60 Oscillator frequencies and their values affect the observer accuracy as highlighted by [6][8]. In addition, the model order 62 is noticeably increased when using KF-Based methods due to augmentation of extra states for the Harmonic Oscillator 64 with the original system states. This adds complexity espe- cially when considering complex PAWEC cases, e.g. multi 66 Degree-Of-Freedom (DOF) PAWECs or PAWEC arrays. The representation of WEF dynamics using harmonic oscillators 68 is unnecessarily complex and other approaches are proposed [10]. These authors describe a receding-horizon approach to 70 estimate the WEF utilizing an iterative solution of a quadratic programming problem shown to give accurate estimation of 72 WEF validated against experimental data. [10] also proposed an estimator using a KF coupled with a Random-Walk WEF 74 model to overcome the complexity of harmonic oscillator WEF representation. The Random-Walk approach shows a 76 comparable performance to the receding-horizon approach but with less complexity and computation burden. 78 As in most scientific studies two approaches to physical modelling usually exist, namely stochastic and deterministic 80 methods. In the context of WEF estimation the former includes the KF as well as the receding horizon approaches discussed 82 above. Here deterministic modelling methods are all based on consideration of non-linear dynamics and uncertainty. For 84 WEF estimation this requires an understanding of the nonlin- ear viscous force effect (see Section II for description) which 86 is shown to be important [11] for accurate PAWEC model utilized for energy maximization control. 88 Motivated by the importance of viscous force considera- tion for model-based energy maximization control and the 90 fact that most of WEF estimator proposed so far have not explicitly consider this important force, this paper proposes a 92 deterministic WEF estimator utilizing the fast unknown input estimation concept. It is worth mentioning that deterministic 94 methods [12], [13] and the stochastic receding-horizon method [10] are based on unknown input estimation as well, but they 96