Resolvent-based tools for optimal estimation and control via the Wiener-Hopf formalism
arXiv:2201.00361 · doi:10.1017/jfm.2022.102
Abstract
The application of control tools to complex flows frequently requires approximations, such as reduced-order models and/or simplified forcing assumptions, where these may be considered low-rank or defined in terms of simplified statistics (e.g. white noise). In this work, we propose a resolvent-based control methodology with causality imposed via a Wiener-Hopf formalism. Linear optimal causal estimation and control laws are obtained directly from full-rank, globally stable systems with arbitrary disturbance statistics, circumventing many drawbacks of alternative methods. We use efficient, matrix-free methods to construct the matrix Wiener-Hopf problem, and we implement a tailored method to solve the problem numerically. The approach naturally handles forcing terms with space-time colour; it allows inexpensive parametric investigation of sensor/actuator placement in scenarios where disturbances/targets are low rank; it is directly applicable to complex flows disturbed by high-rank forcing; it has lower cost in comparison to standard methods; it can be used in scenarios where an adjoint solver is not available; or it can be based exclusively on experimental data. The method is particularly well-suited for the control of amplifier flows, for which optimal control approaches are typically robust. Validation of the approach is performed using the linearized Ginzburg-Landau equation. Flow over a backward-facing step perturbed by high-rank forcing is then considered. Sensor and actuator placement are investigated for this case, and we show that while the flow response downstream of the step is dominated by the Kelvin-Helmholtz mechanism, it has a complex, high-rank receptivity to incoming upstream perturbations, requiring multiple sensors for control.
arXiv comment46 pages, 20 figures. Submitted to the Journal of Fluid Mechanics
References in corpus (16)
- Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
- A critical layer model for turbulent pipe flow
- An Introduction to Adjoint Problems
- Reduced order models for control of fluids using the Eigensystem Realization Algorithm
- Modeling of Transitional Channel Flow Using Balanced Proper Orthogonal Decomposition
- Resolvent-based estimation of space-time flow statistics
- The colour of forcing statistics in resolvent analyses of turbulent channel flows
- Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow
- Resolvent-based estimation of turbulent channel flow using wall measurements
- Efficient computation of global resolvent modes
- Ambiguity in mean-flow-based linear analysis
- Modelling for Robust Feedback Control of Fluid Flows
- Artificial eigenmodes in truncated flow domains
- Feedback control of vortex shedding using a resolvent-based modelling approach
- On the role of actuation for the control of streaky structures in boundary layers
- A realizable data-driven approach to delay bypass transition with control theory
Cited by in corpus (5)
- Towards real-time reconstruction of velocity fluctuations in turbulent channel flow
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- LES-informed resolvent-based estimation of turbulent pipe flow