# Real-Time Wave Energy Converter Control Using Instantaneous Frequency
## 1 Introduction  
Modeling the hydrodynamics of Wave Energy Converters (WECs) is fundamental to the development of effective control strategies. A widely adopted approach is based on the Cummins equation [1, 2], which utilizes convolution integrals to account for fluid memory effects. Although accurate, this method is computationally intensive and complicates real-time determination of hydrodynamic parameters essential for optimizing Power Take-Off Unit (PTO) control. Traditional WEC control techniques, such as passive impedance matching, typically assume a monochromatic wave environment and fixed optimal damping parameters [3]. However, real ocean conditions are broadband and irregular, making static control sub-optimal. Real-time reactive control, which dynamically adjusts PTO damping based on incoming wave characteristics, offers a computationally efficient alternative better suited for such environments [4]. Recently, novel control architectures have explored the use of instantaneous frequency estimation based on the WEC's own velocity signal rather than external wave measurements. [PERSON] et al. [5] proposed an adaptive vector control strategy that monitors the WEC velocity in real time to infer the dominant wave frequency using a Second-Order Generalized Integrator-based Frequency-Locked Loop (SOCI-FLL) structure. By tuning the PTO damping and reactance according to the estimated instantaneous velocity frequency, their method achieves maximum power absorption while mitigating large instantaneous power fluctuations. To support real-time adaptation, various instantaneous frequency estimation methods have been explored, particularly for estimating the excitation force or surface elevation signals. Notable approaches include the Hilbert-Huang Transform (HHT) via Empirical Mode Decomposition (EMD), Frequency-Locked Loop (FLL), and Extended Kalman Filter (EKF) techniques [6]. Beyond frequency estimation, advanced control strategies have been proposed to enhance WEC performance under broadband and irregular sea conditions. For example, [PERSON] et al. [7] introduced a time-varying damping control strategy, originally developed for vibration energy harvesters, which involves modulating the PTO damping coefficient at twice the wave excitation frequency to broaden the energy absorption bandwidth. They also demonstrated that the real-time adaptation of the PTO damping, even without complex predictive models, can significantly improve energy capture in irregular sea states. Recognizing the importance of practical implementation, [PERSON] et al. [8] reviewed simplified WEC control architectures based on impedance matching principles, highlighting the advantages of linear time-invariant (LTI) controllers and straightforward feedback structures suitable for embedded hardware. Experimental validation has substantiated these theoretical findings. [PERSON] et al. [9] demonstrated, using the Pendulum Wave Energy Converter (PeWEC) device, that properly adapting the PTO damping in response to sea states leads to significant improvements in harvested energy. Similarly, [PERSON] et al. [10] confirmed that maximizing energy extraction under broadband spectra requires the real-time adjustment of the PTO force profile. These results underline the practical importance of real-time adaptive damping control and motivate the development of computationally efficient, sensor-based control approaches. Building upon these foundations, the present work proposes a novel extension by investigating real-time instantaneous frequency estimation techniques for practical WEC control. Specifically, this study explores the application of the Hilbert Transform (HT) with median filtering and the Phase-Locked Loop (PLL) methods for real-time frequency tracking and dynamic PTO parameter adaptation.