Resolvent-based approach for H2-optimal estimation and control: an application to the cylinder flow
arXiv:2105.04927 · doi:10.1007/s00162-022-00608-z
Abstract
We consider estimation and control of the cylinder wake at low Reynolds numbers. A particular focus is on the development of efficient numerical algorithms to design optimal linear feedback controllers when there are many inputs (disturbances applied everywhere) and many outputs (perturbations measured everywhere). We propose a resolvent-based iterative algorithm to perform i) optimal estimation of the flow using a limited number of sensors; and ii) optimal control of the flow when the entire flow is known but only a limited number of actuators are available for control. The method uses resolvent analysis to take advantage of the low-rank characteristics of the cylinder wake and solutions are obtained without any model-order reduction. Optimal feedback controllers are also obtained by combining the solutions of the estimation and control problems. We show that the performance of the estimators and controllers converges to the true global optima, indicating that the important physical mechanisms for estimation and control are of low rank.
arXiv comment33 pages, 14 figures
References in corpus (14)
- A critical layer model for turbulent pipe flow
- Reduced order models for control of fluids using the Eigensystem Realization Algorithm
- Modeling of Transitional Channel Flow Using Balanced Proper Orthogonal Decomposition
- Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators
- Resolvent-based estimation of space-time flow statistics
- A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator
- On non-normality and classification of amplification mechanisms in stability and resolvent analysis
- Randomized resolvent analysis
- Resolvent-based estimation of turbulent channel flow using wall measurements
- Efficient white noise sampling and coupling for multilevel Monte Carlo with non-nested meshes
- Energy transfer mechanisms and resolvent analysis in the cylinder wake
- Feedback control of vortex shedding using a resolvent-based modelling approach
- Optimal sensor and actuator placement for feedback control of vortex shedding
- Efficient Solution of Large-Scale Algebraic Riccati Equations Associated with Index-2 DAEs via the Inexact Low-Rank Newton-ADI Method