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Validation des performances des gyroscopes MEMS en utilisant des modèles incertains et temps-variant

Abstract : MEMS gyroscopes are micro sensors that measure the angular rate of an object with respect to a frame of reference, by estimating the Coriolis force. The estimation is obtained thanks to the feedback control of the poorly damped spring-mass system oscillations coupled to synchronous demodulation. In addition to attractive advantages (size, weight, low power consumption and low cost), they suffers of manufacturing dispersion and an important sensitivity to temperature changes. The controllers are designed using strongly simplified models, without a certified performance level. The actual performance of the MEMS is then evaluated through experiments. This PhD work focuses on the pre-experimental performance validation of the designed control, using models that are more realistic, that is a dynamical system analysis problem. Due to synchronous demodulation, the system is modeled as linear system with Harmonically Time-Varying (HTV) parameters, i.e. parameters that are sinusoidal functions of the time. We address the analysis of Linear Harmonically Time-Varying (LHTV) systems by adopting an Integral Quadratic Constraints (IQC) approach. A key step to apply the IQC framework is to characterize HTV parameters by IQCs defined by a set of functions named multipliers. The proper choice of a set of multipliers is crucial with respect to the conservatism of the analysis results. A well-documented case in the literature is the so-called D-G scalings for parametric uncertainties. The D scaling was extended to the HTV case. In this PhD thesis, we investigate the introduction of the G scaling to the HTV case since it dramatically reduces the conservatism in the case of parametric uncertainties.Commercialized MEMS gyroscope must verify accuracy and output noise specifications, defined by standards. We propose model-based performance criteria in order to evaluate these specifications. The most important accuracy specification is the Scale Factor Nonlinearity (SFNL), defined as the maximal gyroscope measurement error for all the measured angular rates. By expressing it as a robust optimization problem, the computation of the SFNL is recast as a convex optimization problem. The proposed approach is validated using experimental results. The standard procedure to evaluate the output noise of MEMS gyroscopes is the Allan variance which is a time-domain statistical tool computed from long-term measures of the gyroscope output. This method allows to classify and quantify the different stochastic processes that are contained in the gyroscope output noise. In order to derive a model-based computation of the Allan variance, we adopt a generator filter approach, which is to our best knowledge original. Different cases are investigated, from LTI models to classes of LHTV models that are relevant for the MEMS gyroscope application, including uncertainties. Convex optimization problems are obtained using e.g. the IQC approach developed for HLTV systems. The proposed approach is validated using experimental results. Finally, the proposed systems analysis tools are applied to the validation of alternative control strategies that require more complex architectures than the classical LTI control.
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https://theses.hal.science/tel-03640679
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Submitted on : Wednesday, April 13, 2022 - 5:52:15 PM
Last modification on : Wednesday, May 18, 2022 - 2:39:20 PM
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  • HAL Id : tel-03640679, version 1

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Jorge Ivan Ayala Cuevas. Validation des performances des gyroscopes MEMS en utilisant des modèles incertains et temps-variant. Autre. Université de Lyon, 2021. Français. ⟨NNT : 2021LYSEC045⟩. ⟨tel-03640679⟩

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