Adapting optimal velocity tracking control to account for WEC constraints and power-take-off efficiencies

Wave energy converters (WECs) come in many different forms, from point absorbers and oscillating water columns to bulge wave devices. This paper focuses on the control of point absorber WECs, which typically have a narrow-banded frequency response and, therefore, control is well placed to improve the energy capture of such WECs. The acausal nature of the control problem means that, theoretically optimal control is almost impossible to achieve in practice; however, optimal velocity tracking (OVT) offers a simple and robust approximation to optimal control that can achieve better power capture than passive linear damping methods, albeit with necessarily higher force demands. OVT is a form of impedance matching and the magnitude of the power-take-off (PTO) force demand is often not linearly proportional to the WEC velocity, which can lead to PTO force and speed combinations far from the optimal PTO efficiency. The highly nonlinear PTO force and speed to efficiency mapping can, without remedial measures, severely diminish the effectiveness of OVT techniques. In this paper, improvements to OVT are made, particularly regarding the limits on motion. In particular, a limit on acceleration is added and drift of the position when the acceleration and/or velocity are limited is prevented through the addition of a new integral term. An anti-wind up methodology to prevent controller integral wind up is also included. These additions allow OVT to be more easily applied in practice. The effect of PTO efficiency is explored, and a novel potential solution to the problem of adapting control to account for efficiency is presented. Both aspects of the work presented highlight the requirement for co-design of the WEC, PTO, and controller.