Two degrees of freedom miniaturized gyroscope based on active magnetic bearings

Thomas Bosgiraud
EPFL, 2008
Thèse EPFL

Résumé

The introduction of the active blocking system, better known as ABS, into cars revealed the growing need for inertial sensing. Among other data, that permit to apprehend the movements of a vehicle, the measurement of the vehicle angular velocity describes the change rate of the vehicle attitude. This measurement has been called by Foucault in 1852 gyroscopic sensing (from the Greek words σκοπειν = observe and γυρος = rotation). The currently available gyroscopes are either very high precision instruments (hence very costly), used in planes, or cheaper products but with a lack of sensitivity to be used in vehicle navigation. Therefore, a real need for gyroscopes combining low cost and precision exists. This thesis proposes to develop a gyroscope based on miniaturized active magnetic bearings (AMB). The advantage of such a device is that the spun mass will be levitated what frees it from any mechanical link to the base of the instrument what render precise classical mechanical gyroscopes so expensive. This thesis presents two prototypes of AMB based gyroscopes. The first one relies on the ball orbit sensing method which is a new theory proposed in this work. Because of the uncertainties due to the nonlinearities inherent to active magnetic bearings, the position of the levitated mass is adaptively controlled. Measurements performed on the prototype have demonstrated the feasibility of this solution with a ball following either a circular or a vertical orbit. The second designed prototype relies on the Newton's second law of motion. Due to the AMB inherent uncertainties and to the force coupling present in the proposed prototype, it has been chosen to drive the levitated mass with a H∞ controller. Simulations are run to compare three different H∞ controllers with the quality of the angular velocity measurement as criterion. Finally, a feed forward H∞ controller showed the best performances in terms of angular velocity measurements during simulations run on the prototype developed during this thesis.

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https://infoscience.epfl.ch/record/124983?ln=fr

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Thomas Bosgiraud
EPFL, 2008
Thèse EPFL

Résumé

Official source

https://infoscience.epfl.ch/record/124983?ln=fr

À propos de ce résultat

Concepts associés (15)

Concepts associés

Chargement

Publications associées (13)

Publications associées

Chargement

Bayesian risk analysis of financial time series

Christophe Osinski

This thesis is a contribution to financial statistics. One of the principal concerns of investors is the evaluation of portfolio risk. The notion of risk is vague, but in finance it is always linked to possible losses. In this thesis, we present some measures allowing the valuation of risk with the help of Bayesian methods. An exploratory analysis of data is presented to describe the sampling properties of financial time series. This analysis allows us to understand the origins of the daily returns studied in this thesis. Moreover, a discussion of different models is presented. These models make strong assumptions on investor behaviour, which are not always satisfied. This exploratory analysis shows some differences between the behaviour anticipated under equilibrium models, and that of real data. The Bayesian approach has been chosen because it allows one to incorporate all the variability, in particular that associated with model choice. The models studied in this thesis allow one to take heteroskedasticity into account, as well as particular shapes of the tails of returns. ARCH type models and models based on extreme value theory are studied. One original aspect of this thesis is its use of Bayesian analysis to detect change points in financial time series. We suppose that a market has two phases, and that it switches from a state to the other at random. Another new contribution is a model integrating heteroskedasticity and time dependence of extreme values, by superposition of the model proposed by Bortot and Coles (2003) and a GARCH process. This thesis uses simulation intensively for the estimation of risk measures. The drawback of simulation is the amount of time needed to obtain accurate estimates. However, simulation allows one to produce results when direct calculation is not feasible. For example, simulation allows one to compute risk estimates for time horizons greater than one day. The methods presented in this thesis are illustrated on simulated data, and on real data from European and American markets. This thesis involved the construction of a library containing C and S code to perform risk analysis using GARCH and extreme value theory models. The results show that model uncertainty can be incorporated, and that risk measures for time horizons greater than one can be obtained by simulation. The methods presented in this thesis have a natural representation involving conditioning. Thus, they permit the computation of both conditional and unconditional risk estimates. Three methods are described: the GARCH method; the two-state GARCH method; and the HBC method. Unconditional risk estimation using the GARCH method is satisfactory on data which seem stationary, but not reliable on data which are non-stationary, such as data with change points. The two-state GARCH model does a little better, but gives very satisfactory results when the risk is estimated conditionally on time. The HBC method does not give satisfactory results.

EPFL2006

Chargement

An optimal prediction problem in financial modelling

Violetta Bernyk

The subject of the present thesis is an optimal prediction problem concerning the ultimate maximum of a stable Lévy process over a finite interval of time. Such "optimal prediction" problems are of both theoretical and practical interest, in particular they have applications in finance. For instance, suppose that an investor has a long position in one financial asset, whose price is modelled by some stochastic process. The investor's objective is to determine a "best moment" at which to close out the position and to sell the asset at the highest possible price. This optimal decision must be based on continuous observations of the asset price performance and only on the information accumulated to date. Hence, the investor should use a prediction (forecasting) of the future evolution of the price of the financial security. We examine this problem in the case where the asset price is modelled by a Lévy process. Indeed, during the last several years, the application of Lévy processes in the modelling financial asset returns has become one of the active research directions in quantitative finance. Thus, this thesis contains suitable new results concerning Lévy processes. We derive the law of the supremum process associated with a strictly stable Lévy process with no negative jumps which is not a subordinator. We note that the latter problem dates back to 1973. In particular, we show that the probability density function of the supremum process can be expressed using an explicit power series representation or via an integral representation. We also derive the infinitesimal generator of the reflected process associated with a general strictly stable Lévy process. Throughout this thesis, we apply the theory of optimal stopping, the methods of fractional differential calculus, and some results from fluctuation theory. Implementing these theories in the context of Lévy processes requires the development of specific analytical results. In the case where the asset price is modelled by a spectrally positive stable Lévy process, we describe the optimal strategy under certain conditions on the model parameters. The optimal strategy is of the following form: the investor must stop the observation of the price process and sell the asset as soon as the associated reflected process crosses for the first time a particular stopping boundary. We also provide numerical estimates and simulation examples of the results obtained by using this strategy.

EPFL2007

Chargement

The possibility to increase the performance (productivity or selectivity) of a chemical reactor by using periodic variations of reaction parameters (e.g. reactant concentration or temperature) has been theoretically envisaged since the beginning of the 70th. The experimental validation of the predicted positive effects was successful in the case of concentration variation but failed for temperature variation. This was mainly due to the high thermal inertia of the conventional chemical reactors used for the measurements which prevented to create variations having a sufficiently high frequency. Microstructure reactors own, at the contrary to conventional reactors, a very low thermal inertia and allow to generate temperature oscillations with an amplitude of about ten to hundred Kelvin at a frequency in the order of magnitude of 10-1 to 4 Hz. These properties, coupled with the possibility to introduce a catalytic active material within the devices, seem to make them well suited for the study of the effects of fast periodic temperature variations of a catalytic reaction. The objective of this work was to demonstrate that non-stationary temperature conditions may increase the reaction rate of a heterogeneously catalyzed reaction up to values not predicted by the classical Arrhenius dependency towards the temperature. Two different types of microstructure reactors have been used. The reaction was taking place in the first one (FTC-type 2) in microstructured channels on whose walls a catalytic layer was deposed. In the second one (FTC-type 3), the reaction was taking place on a piece of sintered metal fibres (SMF) plate placed in a reaction chamber. The catalytic active material was deposed on the SMF plate filaments. Both devices where permanently heated by electrical resistors and periodically cooled down with water flowing through cooling channels incorporated in the devices. The test reaction chosen for the experimental measurements was the CO oxidation reaction, heterogeneously catalyzed by platinum supported on alumina (Pt/Al2O3). The reaction behaviour under stationary thermal conditions was consistent with the one predicted by the Arrhenius law. The dependency of the reaction rate with the temperature was exponential with an apparent activation energy of 104 kJ·mol-1, a negative partial reaction order for CO and a positive one for O2. The measurements effectuated under quasi-stationary thermal conditions (slow temperature ramps) have shown that a temperature change rate between 7 and 14 K·min-1 was not sufficient to observe any non-trivial effect of the temperature. The reaction behaviour was always predicted by the Arrhenius law. The surface coverage of the reactive species is, in this case, always able to follow the slow temperature changes and the reaction behaves as being always under steady-state conditions. The experiments realized under non-stationary thermal conditions using the FTC-type 2 reactor have also failed to demonstrate any non-trivial effects of the temperature oscillations. This device allows indeed to generate temperature oscillations with an amplitude of up to 120 K with a frequency of 0.1 Hz but unfortunately correlated with a very high thermal inhomogeneity. A temperature difference of up to 80 K was measured between a cold spot and a hot spot inside the device. Due to their very low local reaction rate the colder areas of the reactor have attenuated the product concentration (CO2) oscillations which should have been created by the temperature variations. This attenuation prevented the temperature oscillations to have any positive effect compared to the stationary thermal conditions. The FTC-type 3 reactor allowed temperature changes of lower amplitude but the thermal homogeneity was much better. The maximal temperature difference measured between two points within the reactor was only 15 K. Under temperature oscillation conditions, the measured instantaneous CO2 concentration was higher for any temperature within the oscillation range compared to the one recorded under stationary thermal conditions. The increase obtained in the mean CO2 concentration was ranging from 34% for a frequency of the oscillations of 0.035 Hz to 85% for a frequency of 0.052 Hz. The amplitude of the oscillations was kept constant at approximately 40 K and the mean temperature value at 437 K. The simulations effectuated using a theoretical model for the catalytic CO oxidation including a feed-back step in the form of the oxidation-reduction of the catalyst have shown that the experimentally observed increase may be qualitatively explained. Above a certain frequency, the temperature oscillations are fast enough compared to the characteristic time of the feedback step and are able to perturb the stationary established reactive species surface coverage. The formation of a transient surface coverage more favourable for the reaction than the surface coverage at high temperature allows during the transient period to reach an instantaneous surface reaction rate values higher than the one at high temperature. This reaction rate peak is then responsible for the increase of the mean reaction rate under non-stationary thermal conditions and, thus, for an increased yield.

EPFL2008

Chargement

Bayesian risk analysis of financial time series

Christophe Osinski

EPFL2006

An optimal prediction problem in financial modelling

Violetta Bernyk

EPFL2007

EPFL2008