Cross-flow turbines, also known as vertical-axis turbines, have numerous features that make them attractive for wind and marine renewable energy. To maximize power output, the turbine blade kinematics may be controlled during the course of the blade revolution, thus optimizing the unsteady fluid dynamic forces. Dynamically pitching the blades, similar to blade control in a helicopter, is an established method. However, this technique adds undesirable mechanical complexity to the turbine, increasing cost and reducing durability. Here we introduce a novel alternative requiring no additional moving parts: we optimize the turbine rotation rate as a function of blade position resulting in motion (including changes in the effective angle of attack) that is precisely timed to exploit unsteady fluid effects. We demonstrate experimentally that this approach results in a 79% increase in power output over industry standard control methods. Analysis of the fluid forcing and blade kinematics show that maximal power is achieved through alignment of fluid force and rotation rate extrema. In addition, the optimized controller excites a well-timed dynamic stall vortex, as is found in many examples of biological propulsion. This control strategy allows a structurally robust turbine operating at relatively low angular velocity to achieve high efficiency and could enable a new generation of environmentally-benign turbines for wind and water current power generation.

No abstract

No abstract

First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured behavior. Even in mechanical systems, where the equations are assumed to be well-known, there are often model discrepancies corresponding to nonlinear friction, wind resistance, etc. Discovering models for these discrepancies remains an open challenge for many complex systems.In this work, we use the sparse identification of nonlinear dynamics (SINDy) algorithm to discover a model for the discrepancy between a simplified model and measurement data. In particular, we assume that the model mismatch can be sparsely represented in a library of candidate model terms. We demonstrate the efficacy of our approach on several examples including experimental data from a double pendulum on a cart. We further design and implement a feed-forward controller in simulations, showing improvement with a discrepancy model.