This paper addresses the issue of real-time control for applications, subject to physical constraints, involving an energy maximization objective. Typical application areas include renewable energy systems where, in spite of the fact that the raw energy resource is free, the capital and operational costs associated with the energy conversion process are not. In addition, economic energy delivery can only be achieved if the conversion device is operated efficiently. Previous approaches to this problem include model predictive control (MPC), but the computational cost associated with MPC can be high. Pseudospectral solutions show considerable promise in achieving a good balance between performance and computation, but currently available solutions deal with fixed-period optimization. In this paper, a receding horizon real-time pseudospectral control is developed, based on half-range Chebyshev Fourier basis functions, which can accurately represent harmonic signals in the application domain, while also efficiently dealing with the signal truncation effects associated with a receding horizon formulation. An application example, based on a wave energy converter, is used to illustrate the new control algorithm.

In this paper, the effect of non-ideal actuators on the performance of reactive control for a heaving wave energy converter is studied. The concept of the control is to cancel all or part of the reactive terms in the equation of motion. The proposed control is causal, thus it may be applied in practice. Actuators efficiencies from 50 to 100% are considered. The methodology used in the study relies on mathematical and numerical modeling. Control performance is investigated in regular waves and in irregular waves, and also from the perspective of the annual mean absorbed power at a typical Western Atlantic site. Motion constraints are not taken into account in the analysis for sake of simplicity. As already shown in previous work, it is found that reactive control can increase the mean annual power absorption at the considered site by a factor 10 in case of ideal actuators. However, it is shown that actuators efficiency is critical to control performance, because of the large amount of reactive power involved in the control strategy. Thus, for low efficiencies actuators (<80%), control performance is a fraction of what it can be with ideal actuators (approximately 10%). Even with 90% efficiency, control performance is less than 30% of the ideal case. In the range 90-100%, every percent of increase in efficiency leads to significant increase in control performance.

Wave energy converters (WECs) require active control to maximise energy capture over a wide range of sea conditions, which is generally achieved by making the device resonate. The exaggerated device motion arising at resonance, however, may result in nonlinear effects that are ignored by the linear models that are typically employed. In particular, nonlinear viscous forces are significant for particular device types, such as hinged flaps, which we take as a case study in this paper. The paper develops a general nonlinear WEC control methodology based on pseudospectral methods. The continuous time energy maximisation problem is fully discretised (both state and control), and the optimal solution is obtained by solving the resulting finite dimensional optimisation problem. By way of example, the nonlinear viscous damping for a hinged flap WEC is incorporated into the control model which also considers non-ideal power takeoff efficiency. It is shown that the ratio of energy captured to energy dissipated is significantly increased with the nonlinear controller, compared to the linear case.

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