Control Co-design of a Hydrokinetic Turbine: A Comparative Study of Open-loop Optimal Control and Feedback Control

TL;DR

This work extends control co-design (CCD) to include realizable feedback controllers for hydrokinetic turbines (HKT), comparing open-loop optimal control (OLOC) with linear and quadratic state-feedback laws. It shows that a $u\_q=K\omega^2$ feedback law can closely replicate the OLOC trajectory while enabling simpler, more robust real-time control, even under uncertainty and with a control-load constraint. The study demonstrates that the quadratic feedback architecture yields comparable energy output to OLOC and superior robustness to flow disturbances, with only minimal degradation in energy when constraints are present. Overall, the findings highlight the value of incorporating feedback control explicitly in the CCD stage to achieve near-optimal, robust, and practically implementable HKT designs.

Abstract

Control co-design (CCD) explores physical and control design spaces simultaneously to optimize a system's performance. A commonly used CCD framework aims to achieve open-loop optimal control (OLOC) trajectory while optimizing the physical design variables subject to constraints on control and design parameters. In this study, in contrast with the conventional CCD methods based on OLOC schemes, we present a CCD formulation that explicitly considers a feedback controller. In the formulation, we consider two control laws based on proportional linear and quadratic state feedback, where the control gain is optimized. The simulation results show that the OLOC trajectory could be approximated by a feedback controller. While the total energy generated from the CCD with a feedback controller is slightly lower than that of the CCD with OLOC, it results in a much simpler control structure and more robust performance in the presence of uncertainties and disturbances, making it suitable for real-time control. The study in this paper investigates the performance of optimal hydrokinetic turbine design with a feedback controller in the presence of uncertainties and disturbances to demonstrate the benefits and highlight challenges associated with incorporating the feedback controller explicitly in the CCD stage.

Figures (12)

• Figure 1: The notional representation of blade geometry and model in BEM. $c$: chord length, $\alpha$: twist angle, and $dr$: length of discretized elements along radius.
• Figure 2: Schematic of the CCD optimization process.
• Figure 3: Control load (top) and HKT rotating speed (bottom) for CCD with OLOC, linear feedback, and quadratic feedback, optimized for inflow condition defined in (\ref{['eq:simple_flow']}) .
• Figure 4: Comparison of physical geometry optimized by CCD with OLOC, and linear and quadratic feedback controllers, as well as the baseline design without constraint on control for inflow condition defined in (\ref{['eq:flow_sin_base']}). (top) twist angle, and (bottom) chord length.
• Figure 5: Power coefficients versus TSR for CCD optimization with OLOC, linear and quadratic feedback with no constraint on control load.