Nested Plant/Controller Co-Design Using G-Optimal Design and Extremum Seeking: Theoretical Framework and Application to an Airborne Wind Energy System

Abstract This paper presents a unique nested optimization framework for the co-design of a physical system (plant) and controller, which leverages optimal Design of Experiments (DoE) techniques for the plant optimization and extremum seeking for the control system optimization. At each iteration of the optimization, candidate plant parameters are generated by using G-optimal DoE. Unlike gradient-based approaches, the use of optimal DoE enables efficient global exploration of a plant design space that can contain multiple local optima. For each candidate plant design, the corresponding controller optimization is performed in real time, using extremum seeking. This enables the real-time adjustment of controller parameters during the course of simulations or experiments, thereby expediting the overall optimization process. The co-design process is carried out iteratively, where sub-optimal plant designs are rejected based on a response surface characterization and hypothesis testing. The co-design framework was validated in simulation for a Buoyant Airborne Turbine (BAT). Here, the optimized plant parameters were a reference area scale factor (scales the horizontal and vertical stabilizer areas uniformly) and center of mass location, whereas the optimized control parameter was the pitch angle setpoint. After four complete iterations, the flight performance index improved and the feasible plant design space (i.e., the locus of plant design parameters that could possibly be optimal, based on hypothesis testing) shrunk by 99%.