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Modelling for Flight Control

Auger D.J.

July 2005

Abstract

This dissertation considers model (in)validation in the context of closed-loop control. Real-world data invariably differs from that predicted by mathematical models. Discrepancies are due to modelling inaccuracy or exogenous noise. We address the question of whether given data is consistent with a member of a model set consisting of a 'ball' of systems in Vinnicombe's nu-gap metric. Existence can be determined using tangential Carathéodory-Fejér interpolation techniques, however the full necessary and sufficient conditions are non-convex in the presence of noise. In previous work, e.g. by Steele and Vinnicombe, these conditions are approximated to give sufficient conditions for consistency. This work proposes a technique for improving these approximations by successive relinearization about previous solutions, extends this to systems with non-zero initial conditions and proposes techniques for the construction of interpolants using Nevanlinna-Pick methods.

The work also considers an approach put forward by Smith, Dullerud and Miller in which Yakubovich's S-procedure is applied to problems with linear time-varying perturbations. A claimed necessary and sufficient condition for invalidation is shown to be sufficient only, a tighter sufficient condition is put forward, and a similar condition for non-causal perturbations is proposed.

Finally, model (in)validation techniques are applied to flight test data from QinetiQ's VAAC Harrier. Two experiments are performed on the longitudinal dynamics with different signal injection points. The techniques are seen to work effectively for both, though one experiment is considered more informative than the other. When the initial state is fixed at zero causality and time-invariance are significant constraints but when the initial state can vary only time-invariance is significant. Two dynamic weighting strategies are considered, one based on the frequency-wise optimal stability margin, the other on a simplified 'proportional integral' approximation with the same all-frequency stability properties. These give consistent results. Interpolants are constructed and found to have unrealistically non-smooth frequency responses.

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BibTex Entry

@PhdThesis{auger2005:_modelling_for_flight_control,: author = {Auger D.J.},; school = {University of Cambridge},; title = {Modelling for Flight Control},; year = {2005},; bibkey = {auger2005:_modelling_for_flight_control},; month = {July}
}



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