This article examines the use of actively controlled electronics to maximize the energy harvested from a stationary stochastic disturbance. In prior work by the authors, it has been shown that when the harvester dynamics are linear and the transmission losses in the electronics are resistive, the optimal feedback controller is the solution to a nonstandard linear-quadratic-Gaussian optimal control problem. This article augments the theory in the following three distinct ways: (a) It illustrates how to use linear matrix inequalities to balance the objective of energy harvesting against other response control objectives (such as minimum requirements on closed-loop damping and maximum levels of voltage response), in the synthesis of the optimal feedback law; (b) it establishes a more realistic characterization of the transmission losses in the actively controlled power electronics used to regulate the extraction of power; and (c) it illustrates how the optimal control theory for resistive loss models can be extended to accommodate the more realistic loss models. The theory is illustrated in the context of a piezoelectric energy harvesting model, and an example is used to illustrate that the theory can be used to simultaneously optimize the feedback law, together with the switching frequency and storage bus voltage of the power electronics.

We consider feedback control design for a wave energy converter (WEC) for which the power takeoff (PTO) system has a finite stroke limit. Stationary stochastic wave loading is assumed, with a known spectrum, and the plant dynamics are assumed to be linear. We develop a technique for the design of a discrete-time controller, which has three design stages. In the first stage, a linear controller is optimized while imposing a relaxation of the maximum stroke constraint on the design. In the second stage, a tandem nonlinear feedback loop is designed for the purpose of stroke protection. In the third stage, the two designs (linear and nonlinear) are fused in a manner that preserves the stability of the overall system. The technique is demonstrated in a simulation of a simple cylindrical buoy. We show that the controller may be tuned through the adjustment of scalar design parameters, which adjust the tradeoff between the mean generated power and the force levels required to protect the stroke.

We implement a causal model predictive control (MPC) strategy to maximize power generation from a wave energy converter (WEC) system, for which the power take-off (PTO) systems have both hard stroke (i.e., displacement) limits and force ratings. The approach models the WEC dynamics in discrete time, in a manner that exactly preserves energy flow quantities, and assumes a stationary stochastic disturbance model for the incident wave force. The control objective is to maximize the expected power generation in stationarity, while accounting for parasitic losses in the power train. PTO stroke measurements are assumed to be available for real-time feedback, as well as the free surface elevation of the waves at a designated location relative to the WEC, and the open-loop dynamics of the WEC are assumed to be linear and time invariant. Mean-square stability of the MPC algorithm is proven. The methodology is illustrated in a simulation example pertaining to a heaving cylindrical buoy.

Efforts by various researchers in recent years to design simple causal control laws that can be applied to WEC devices suggest that these controllers can yield similar levels of energy output as those of more complex non-causal controllers. However, most studies were established without adequately considering device and power conversion system constraints which are relevant design drivers from a cost and economic point of view. It is therefore imperative to understand the benefits of MPC compared to causal control from a performance and constraint handling perspective. In this paper, we compare linear MPC to a casual controller that incorporates constraint handling to benchmark its performance on a one DoF heaving point absorber in a range of wave conditions. Our analysis demonstrates that MPC provides significant performance advantages compared to an optimized causal controller, particularly if significant constraints on device motion and/or forces are imposed. We further demonstrate that distinct control performance regions can be established that correlate well with classical point absorber and volumetric limits of the wave energy conversion device.

In energy harvesting technologies, the circuitry used to extract power can be viewed as imposing a feedback law on the harvester's dynamics. Each circuit topology affords some degree of controllability, and consequently, a feasibility domain over which its feedback law can be optimized to maximize the harvested energy. The parasitic losses associated with a given circuit can be large enough that they are comparable to or exceed the available resource, thus precluding its viability. This article examines these issues for single-degree-of-freedom vibration energy harvesters subjected to a single-impulsive inertial loading. We introduce two different quadratic overbound techniques for parasitic loss modeling: one based on physical circuit parameters and the other based on a static efficiency model. We consider the choice between an active rectifier and active drive circuit to condition the power, and also the choice of whether to include power-factor correction circuitry. The four resultant design combinations represent different tradeoffs between the control functionality and the parasitic loss. For all cases, we illustrate a technique for determining the maximum energy that can be harvested from the impulse using the optimal control theory. We then use this analysis to determine, for each case, whether the parasitic power it must sustain to operate is justified by the performance it achieves. We also determine the critical threshold of parasitic loss, below which a given case is not a viable technology. Finally, we show that the relative favorability of each circuit depends strongly on the characteristics of the harvesting device, as well as the disturbance intensity.