Control of the Fluidic Pinball using the Quadratic-Quadratic Regulator

Ali Bouland, Jeff Borggaard

Abstract

In control of fluid dynamics, the fluidic pinball problem presents a significant benchmark problem. This problem seeks to control the vortex shedding behind three cylinders using cylinder rotation as the actuation mechanism and drive it to a desired steady-state solution. This talk describes a novel model-based approach that combines the Quadratic-Quadratic Regulator (QQR) [Borggaard and Zietsman, 2020] feedback control methodology with interpolatory model order reduction to address this challenge. The QQR is based on finding polynomial approximations to the Hamilton-Jacobi-Bellman equations, that can serve as a Lyapunov function and be used to develop polynomial feedback control laws. This approach is demonstrated for two different Reynolds numbers, Re_D = 30 and Re_D = 50. In the case of Re_D = 30, the QQR controller is able to control the system and achieves the desired performance criteria 40.1% faster than the linear controller. In the case of Re_D = 50, only the QQR controller successfully controls the flow, while the linear controller fails.