The University of Maynooth is hosting a competition to develop a control strategy for a heaving point absorber wave energy converter (WEC). A linear model predictive control (MPC) design for the competition is presented. The state space model used in the MPC was derived numerically from the provided WEC-Sim model using linear system identification methods. A Kalman filter was used as the estimator, while also serving as an unknown input estimator to provide estimates of the excitation force on the WEC. The required excitation force predictions were made using an autoregressive linear prediction model. The inputs to the prediction model included estimated wave excitation forces and measured water surface elevation values from an up-field wave probe. Simulation results of the final control system design are also presented for each of the six wave cases specified by the competition organizers.