This work is located in a growing sector within the field of renewable energies, wave energy converters (WECs). Specifically, it focuses on one of the point absorber waves (PAWs) of the hybrid platform W2POWER. With the aim of maximizing the mechanical power extracted from the waves by these WECs and reducing their mechanical fatigue, the design of five different model predictive controllers (MPCs) with hard and soft constraints has been carried out. As a contribution of this paper, two of the MPCs have been designed with the addition of an embedded integrator. In order to analyze and compare the MPCs with conventional PI type control, an exhaustive study about performance and robustness is realized through the computer simulations carried out, in which uncertainties in the WEC dynamics and JONSWAP spectrum are considered. The results obtained show how the MPCs with embedded integrator improve power production of the WEC system studied in this work.