Experimental control of Tollmien–Schlichting waves using pressure sensors and plasma actuators

Brito, Pedro P. C.; Morra, Pierluigi; Cavalieri, André V. G.; Araújo, Tiago Barbosa de; Henningson, Dan S.; Hanifi, Ardeshir

doi:10.1007/s00348-020-03112-4

Cited by 9 publications

(8 citation statements)

References 51 publications

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“…The kernels that were obtained in § 2.5, and as will be shown in § 4, are smooth and decay rapidly for large values of τ . This means that the convolutions required for estimation and control can be efficiently computed with a finite number of points using standard numerical quadrature methods, and, thus, can be used in implementations with limited memory and computational power, as in experimental applications (Fabbiane et al 2015;Brito et al 2021;Maia et al 2021).…”

Section: Discussionmentioning

confidence: 99%

“…It does, however, provide upper bounds for the effectiveness of causal control, and it is the basis for the control method proposed by Sasaki et al (2018b), where the kernel is truncated to its causal part. This approach was also successfully applied to experiments (Brito et al 2021;Maia et al 2021). However, truncating the non-causal control kernel is, in general, sub-optimal.…”

Section: Partial-knowledge Controlmentioning

confidence: 98%

“…Three control approaches are explored: non-causal control (nc), the truncated non-causal control (tnc) and optimal-causal control (c). Truncated non-causal control corresponds to a truncation of the optimal non-causal control to its causal part, corresponding to the approach used in previous works (Sasaki et al 2018b;Brito et al 2021), which was seen, in some cases, to be a good approximation for optimal causal control, pointing to a wave-cancelling nature of optimal control strategies in these scenarios (Sasaki et al 2018a). Non-causal control cannot be used in real-time applications, but it provides upper bounds for the performance of any linear control strategy and, thus, can be useful to evaluate different sensor and actuator placements.…”

Section: Control With a Single Sensormentioning

confidence: 99%

“…This has been shown to closely reproduce optimal control when there is sufficient distance between sensors, actuators and targets (Sasaki et al 2018a). While this can significantly reduce the effectiveness of the controller (Brito et al 2021), the approach has been successfully used in numerous studies (Hanson et al 2014;Sasaki et al 2018b;Maia et al 2021). A similar approach was used by Luhar et al (2014), where opposition control based on the resolvent operator was performed.…”

Section: Introductionmentioning

confidence: 99%

“…This construction provides physical insights on the structures that can be estimated and controlled. The approach can also be used to improve wave-cancelling strategies (Li & Gaster 2006;Fabbiane et al 2014;Sasaki et al 2018a;Brito et al 2021;Maia et al 2021), minimizing the effect of kernel truncation.…”

Section: Introductionmentioning

confidence: 99%

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Resolvent-based tools for optimal estimation and control via the Wiener–Hopf formalism

et al. 2022

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Partial-knowledge Controlmentioning

confidence: 98%