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Uncertainty propagation in model extraction by system identification and its implication for control design

Published online by Cambridge University Press:  17 February 2016

Nicolas Dovetta ,
Peter J. Schmid  and
Denis Sipp
Nicolas Dovetta*
Affiliation:
Laboratoire d’Hydrodynamique (LadHyX), Ecole Polytechnique, F-91128 Palaiseau, France
Peter J. Schmid
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Denis Sipp
Affiliation:
ONERA-DAFE, 8 rue des Vertugadins, F-92190 Meudon, France
*
†Email address for correspondence: [email protected]
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Abstract

In data-based control design, system-identification techniques are used to extract low-dimensional representations of the input–output map between actuators and sensors from observed data signals. Under realistic conditions, noise in the signals is present and is expected to influence the identified system representation. For the subsequent design of the controller, it is important to gauge the sensitivity of the system representation to noise in the observed data; this information will impact the robustness of the controller and influence the stability margins for a closed-loop configuration. Commonly, full Monte Carlo analysis has been used to quantify the effect of data noise on the system identification and control design, but in fluid systems, this approach is often prohibitively expensive, due to the high dimensionality of the data input space, for both numerical simulations and physical experiments. Instead, we present a framework for the estimation of statistical properties of identified system representations given an uncertainty in the processed data. Our approach consists of a perturbative method, relating noise in the data to identified system parameters, which is followed by a Monte Carlo technique to propagate uncertainties in the system parameters to error bounds in Nyquist and Bode plots. This hybrid approach combines accuracy, by treating the system-identification part perturbatively, and computational efficiency, by applying Monte Carlo techniques to the low-dimensional input space of the control design and performance/stability evaluation part. This combination makes the proposed technique affordable and efficient even for large-scale flow-control problems. The ARMarkov/LS identification procedure has been chosen as a representative system-identification technique to illustrate this framework and to obtain error bounds on the identified system parameters based on the signal-to-noise ratio of the input–output data sequence. The procedure is illustrated on the control design for flow over an idealized aerofoil with a trailing-edge splitter plate.

JFM classification

Mathematical Foundations: Computational methods Flow Control: Control theory Flow Control: Flow Control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , pp. 214 - 236
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Copyright
© 2016 Cambridge University Press 

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