Suboptimal control of circular cylinder wakes using Van der Pol oscillator

• Published in: Computers & fluids 2019-01, Vol.179, p.15-26
• Main Authors: Das, Pramode K., Vijay Anand, D., Shaiju, A.J., Patnaik, B.S.V.
• Format: Article
• Language: English
• Subjects: Circular cylinder; Circular cylinders; Computational fluid dynamics; Computer simulation; Control systems design; Controllers; Dynamic models; Energetic efficiency; Navier-Stokes equations; Parameter estimation; Pontryagin’s minimum principle; Power efficiency; Power loss; Reduced order models; Suboptimal control; Subspace methods; Van der Pol oscillator; Vortex shedding; Wakes
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2018.10.011

•The Van der Pol oscillator is employed as a reduced-order model for the control optimization of cylinder wakes.•A subspace identification strategy is used to relate the inputs to the higher dimensional model and the reduced-order model.•Suitable tracking and regulator problems are designed and resolved to determine the optimal controls.•An open-loop optimal controller that generates the dynamic features of the closed-loop integral controller is developed.•The optimal controller was found to successfully control vortex shedding behind a cylindrical structure.•A plausible explanation for the flow control mechanism in terms of mechanical energy and work is provided. In the present study, we develop an energetically efficient suboptimal open-loop strategy to control the wake behind a circular cylinder in the laminar regime. The open-loop suboptimal controller is designed to resemble the feedback integral controller with reference to its dynamical behaviour. Energetic efficiency is measured using the power loss coefficient. The Van der Pol model for the evolution of lift force on the cylinder is chosen as the reduced-order model for the development of an open-loop suboptimal controller. The parameter estimation of the low- dimensional model is carried out using the results from the continuum based Navier - Stokes simulations. It is shown that a subspace identification method can be used to model the relationship between the inputs to the reduced-order model and the inputs to the higher-order computational fluid dynamic model. The development of the suboptimal control is realised by means of solving suitably formulated optimal tracking and regulator problems using the Pontryagin’s minimum principle. The resultant controller is found to be energetically efficient and also successful in the control of vortex shedding.