Improving the power production in wave energy plants is essential to lower the cost of energy production from this type of installations. Oscillating Water Column is among the most studied technologies to convert the wave energy into a useful electrical one. In this paper, three control algorithms are developed to control the biradial turbine installed in the Mutriku Wave Power Plant. The work presents a comparison of their main advantages and drawbacks first from numerical simulation results and then with practical implementation in the real plant, analysing both performance and power integration into the grid. The wave-to-wire model used to develop and assess the controllers is based on linear wave theory and adjusted with operational data measured at the plant. Three different controllers which use the generator torque as manipulated variable are considered. Two of them are adaptive controllers and the other one is a nonlinear Model Predictive Control (MPC) algorithm which uses information about the future waves to compute the control actions. The best adaptive controller and the predictive one are then tested experimentally in the real power plant of Mutriku, and the performance analysis is completed with operational results. A real time sensor installed in front of the plant gives information on the incoming waves used by the predictive algorithm. Operational data are collected during a two-week testing period, enabling a thorough comparison. An overall increase over 30% in the electrical power production is obtained with the predictive control law in comparison with the reference adaptive controller. (C) 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).