Force-Limited Control of Wave Energy Converters using a Describing Function Linearization

Abstract

Actuator saturation is a common nonlinearity. In wave energy conversion, force saturation conveniently limits drivetrain size and cost with minimal impact on energy generation. However, such nonlinear dynamics typically demand numerical simulation, which increases computational cost and diminishes intuition. This paper instead uses describing functions to approximate a force saturation nonlinearity as a linear impedance mismatch. In the frequency domain, the impact of controller impedance mismatch (such as force limit, finite bandwidth, or parameter error) on electrical power production is shown analytically and graphically for a generic nondimensionalized single degree of freedom wave energy converter in regular waves. Results are visualized with Smith charts. Notably, systems with a specific ratio of reactive to real mechanical impedance are least sensitive to force limits, a criteria which conflicts with resonance and bandwidth considerations. The describing function method shows promise to enable future studies such as large-scale design optimization and co-design.

Figures (7)

• Figure 1: Thévenin equivalent circuit for linear system
• Figure 2: Smith chart showing average power, using (\ref{['eq:ratio-power']}).
• Figure 3: Smith charts showing the (a) peak voltage and (b) peak current at the load for any $z=Z_L/Z_{th}^*$, paired with (c) the pareto tradeoff between voltage, current, and power. The Thévenin reactance parameter $\alpha$ is swept. Shaded regions indicate that the voltage (green) or current (pink) ratios exceed one. Dashed lines are optimal contours.
• Figure 4: Pareto front for optimal voltage and current ratios.
• Figure 5: Block diagram of dynamics.