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Optimal sensor and actuator placement for feedback control of vortex shedding

Published online by Cambridge University Press:  02 December 2021

Bo Jin Open the ORCID record for Bo Jin [Opens in a new window] ,
Simon J. Illingworth Open the ORCID record for Simon J. Illingworth [Opens in a new window]  and
Richard D. Sandberg Open the ORCID record for Richard D. Sandberg [Opens in a new window]
Bo Jin*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, VIC 3010, Australia
Simon J. Illingworth
Affiliation:
Department of Mechanical Engineering, University of Melbourne, VIC 3010, Australia
Richard D. Sandberg
Affiliation:
Department of Mechanical Engineering, University of Melbourne, VIC 3010, Australia
*
†Email address for correspondence: bjin1@student.unimelb.edu.au
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Abstract

We consider linear feedback control of the two-dimensional flow past a cylinder at low Reynolds numbers, with a particular focus on the optimal placement of a single sensor and a single actuator. To accommodate the high dimensionality of the flow, we compute its leading resolvent forcing and response modes to enable the design of $\mathcal {H}_2$-optimal estimators and controllers. We then investigate three control problems: (i) optimal estimation (OE) in which we measure the flow at a single location and estimate the entire flow; (ii) full-state information control (FIC) in which we measure the entire flow but actuate at only one location; and (iii) the overall feedback control problem in which a single sensor is available for measurement and a single actuator is available for control. We characterize the performance of these control arrangements over a range of sensor and actuator placements and discuss implications for effective feedback control when using a single sensor and a single actuator. The optimal sensor and actuator placements found for the OE and FIC problems are also compared with those found for the overall feedback control problem over a range of Reynolds numbers. This comparison reveals the key factors and conflicting trade-offs that limit feedback control performance.

JFM classification

Flow Control: Control theory Vortex Flows: Vortex shedding Vortex Flows: Vortex instability

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JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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