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Sensor and actuator placement trade-offs for a linear model of spatially developing flows

Published online by Cambridge University Press:  31 August 2018

Stephan F. Oehler Open the ORCID record for Stephan F. Oehler [Opens in a new window]  and
Simon J. Illingworth Open the ORCID record for Simon J. Illingworth [Opens in a new window]
Stephan F. Oehler*
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
Simon J. Illingworth
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
*
†Email address for correspondence: stephan.friedrich.oehler@gmail.com
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Abstract

We consider feedback flow control of the linearised complex Ginzburg–Landau system. The particular focus is on any trade-offs present when placing a single sensor and a single actuator. The work is presented in three parts. First, we consider the estimation problem in which a single sensor is used to estimate the entire flow field (without any control). Second, we consider the full information control problem in which the entire flow field is known, but only a single actuator is available for control. By considering the optimal sensor placement and optimal actuator placement while varying the stability of the system, a fundamental trade-off for both problems is made clear. Third, we consider the overall feedback control problem in which only a single sensor is available for measurement; and only a single actuator is available for control. By varying the stability of the system, similar fundamental trade-offs are made clear. We discuss implications for effective feedback control with a single sensor and a single actuator and compare it to previous placement methods.

JFM classification

Flow Control: Control theory Flow Control: Flow Control Flow Control: Instability control

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JFM Papers
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Journal of Fluid Mechanics , Volume 854 , 10 November 2018 , pp. 34 - 55
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© 2018 Cambridge University Press 

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