Confirmation of a Nonlinear Model Predictive Control Strategy Applied to a Permanent Magnet Linear Generator for Wave-Energy Conversion

This paper begins with a brief review of the time-domain equation of motion for a generic floating body. The equation of motion of the floating body was modified to account for the influence of a power-take-off unit (PTO) to predict the hydrodynamic and electromechanical performance of the coupled system. As the damping coefficient is considered the dominant contribution to the PTO reaction force, the optimum non time-varying damping values were first presented for all frequencies, recovering the well-known impedance-matching principle at the coupled resonance frequency. In an effort to further maximize power absorption in both regular and irregular wave environments, nonlinear model predictive control (NMPC) was applied to the model-scale point absorber developed at UC Berkeley. The proposed NMPC strategy requires a PTO unit that could be turned on and off instantaneously, leading, interestingly to electrical sequences where the generator would be inactive for up to 60% of the wave period. In order to validate the effectiveness of this NMPC strategy, an in-house designed permanent magnet linear generator (PMLG) was chosen as the PTO. The time-varying performance of the PMLG was first characterized by dry-bench tests, using mechanical relays to control the electromagnetic conversion process. Following this, the physical set-up was transferred to the wave tank. The on/off sequencing of the PMLG was tested under regular and irregular wave excitation to validate NMPC simulations using control inputs obtained from running the control algorithm offline. Experimental results indicate that successful implementation was achieved and the absorbed power using NMPC was up to 50% greater than the passive system, which utilized no controller. However, after considering the PMLG mechanical-to-electrical conversion efficiency the useful electrical power output was not consistently maximized. To improve output power, a mathematical relation between the efficiency and damping magnitude of the PMLG was inserted in the system model to maximize the electrical power output through continued use of NMPC. Of significance, results from these latter simulations provided a damping time series that was active over a larger portion of the wave period and required the actuation of the applied electrical load connected to the PMLG, rather than a simple on/off type control.