An Efficient Convex Formulation for Model-Predictive Control on Wave-Energy Converters

Model-Predictive Control (MPC) has shown its strong potential in maximizing energy extraction for Wave-Energy Converters (WECs) while handling hard constraints. As MPC can solve the optimization problem on-line, it can better account for state changes and reject disturbances from the harsh sea environment. Interests have arisen in applying MPC to an array of WECs, since researchers found that multiple small-size WECs are more economically viable than a single large-size WEC. However, the computational demand is known to be a primary concern for applying MPC in real-time, which can determine the feasibility of such a controller, particularly when it comes to controlling an array of absorbers. In this paper, we construct a cost function and cast the problem into a Quadratic Programming (QP) with the machinery force being the “optimizer,” for which the convexity can be guaranteed by introducing a penalty term on the slew rate of the machinery force. The optimization problem can then be solved efficiently, and a feasible solution will be assured as the global optima. Constraints on the motion of the WEC and the machinery force will be taken into account. The current MPC will be compared to others existing in literature, including a nonlinear MPC [1] which has been applied in wave-tank tests. The effects of constraints on the control law and the absorbed power are investigated. Performances of the WEC are shown for both regular and irregular wave conditions. The current MPC is found to have good energy-capture capability and is able to broaden the band-width for capturing wave energy. The reactive power required by the PTO system is presented. The additional penalty term provides a tuning parameter, of which the effects on the MPC performance and the reactive power requirement are discussed.