Bernard Vau:
- PhD in Control Science
- Senior Control Expert at Exail (Paris area)
This page presents my research achievements (both industrial and academic), in particular those resulting from a PhD thesis carried out from 2015 to 2019 at SATIE (Ecole Normale Superieure de Paris-Saclay, France), under the direction of Henri Bourlès. I continue to do advanced research in automatic control, in addition to my professional practice. Collaborations with Professors Ioan-Doré Landau (CNRS Grenoble), Henri Bourlès (SATIE ENS Paris-Saclay), Tudor-Bogdan Arimitoaie (Bordeaux University).
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- Ioan Doré Landau, Tudor Bogdan Airimitoaie, Bernard Vau, Gabriel Buche, « On a general structure for adaptation/learning algorithms — Stability and performance issues », Automatica (Elsevier), vol.156, October 2023.
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The paper introduces a general structure for parameter adaptation/learning algorithms (PALA). This structure is characterized by the presence of an embedded ARMA (poles-zeros) filter in the PALA. The key question is how to select the coefficients of this filter in order, on the one hand, to guarantee the stability of the parameter estimator for any (positive) value of the adaptation gain/learning rate and for any initial conditions and on the other hand to accelerate the adaptation transient. In order to achieve this, it is shown that on one hand the embedded ARMA filter should be characterized by a positive real transfer function and on the other hand the filter acting on the correcting term (the dynamic adaptation gain) should be characterized by a strictly positive real transfer function. Specific conditions for the design of a second order ARMA embedded filter (ARIMA2 algorithm) are provided.It is shown in the paper that many parameter adaptation/learning algorithms (PALA) used in adaptive control, system identification and neural networks (Nesterov, Conjugate gradients, Momentum back propagation, Averaged gradient, Integral+proportional+derivative, …) are particular cases of the PALA structure introduced in this paper and specific conditions for the stable operation of these algorithms are given. Performance of the ARIMA2 algorithm as well as of the other algorithms reviewed in the paper will be comparatively evaluated by simulations and experimental results obtained on an active noise control system.
- Ioan Doré Landau, Bernard Vau, Tudor Bogdan Airimitoaie, Gabriel Buche, « Improving performance of adaptive feedforward noise attenuators using a dynamic adaptation gain », Journal of Sound and Vibration (Elsevier), vol.560, May 2023. View
The paper explores in detail the use of dynamic adaptation gain/learning rate (DAG) for improving the performance of adaptive feedforward attenuation schemes. The DAG is an ARMA (poles-zeros) filter embedded in gradient type adaptation/learning algorithms and generalizes the various improved gradient algorithms available in the literature. After introducing the DAG algorithm in the context of adaptive feedforward attenuation schemes and providing relation- ships with other algorithms, its design is developed. Strictly Positive Real (SPR) conditions play an important role in the design of the DAG. Then the stability issues for adaptive/learning systems using a DAG are discussed. The potential of the DAG is then illustrated by experimental results obtained on a relevant adaptive active noise control system.
- Ioan Doré Landau, Bernard Vau, Gabriel Buche, « Recursive Algorithms for Identification of Dual Youla-Kucera Parametrized Plant Models in Closed Loop », European Journal of Control (Elsevier), vol.139, September 2022. View
The growing interest in using dual Youla Kucera plant parametrization for modeling plant uncertainties raises the need for recursive identification algorithms dedicated to the identification of these structures in closed loop in view of developing appropriate iterative tuning and adaptive control strategies. The paper presents recursive algorithms for identification in closed loop of dual Youla-Kucera parametrized plant models. These algorithms assure global asymptotic stability in the deterministic environment and allow to obtain unbiased parameter estimation in the presence of measurement noise when the plant model is in the model set. The paper also re-visit the Hansen scheme which allows to associate open loop type recursive identification algorithms for the identification of these structures in closed loop. When the plant model is not in the model set, comparison of the various algorithms is done in terms of the bias distribution. Further comparisons and performance evaluation is provided by simulations on some relevant examples and experimental identification in closed loop of a test bench for active noise control.
- Bernard Vau, Henri Bourlès, « A robust whitness test for the identification of discrete-time linear models: Use of orthonormal transfer functions », Automatica (Elsevier), vol.139, May 2022. View
A novel whiteness test of residuals is proposed, which makes use of generalized bases of orthonormal transfer functions. It can be viewed as a robustified version of the classical whiteness test in the sense that it reduces the risk of type II errors, by introducing a frequency weighting in the assessment of the flatness in the residual power spectrum density. This frequency weighting, which depends on the basis poles, can be employed for the validation of reduced order models, when the flatness of the residual power spectrum density is evaluated over a limited frequency band.
- Gabriel Buche, Bernard Vau, Ioan Doré Landau, Raul Melendez, « Handling large model uncertainty in adaptive feedback noise attenuation by overparametrization », Journal of Sound and Vibration (Elsevier), vol. 509, September 2021. View
Adaptive feedback noise attenuation is a very efficient way of strongly attenuating multiple tonal and narrow band disturbances with unknown and time varying characteristics. These adaptive schemes implement the internal model principle (IMP) for canceling disturbances combined with the Youla Kucera (YK) parametrization which allows to directly tune the disturbance compensation filter without explicit identification of the disturbance model. Efficient use of these schemes requires a good knowledge of the compensatory path model, which can be obtained by experimental system identification. However, there are potential applications where the characteristics of the compensatory path may change significantly during operation and this may lead to the instability of the system. The paper addresses the problem of handling large plant model uncertainties by overparametrization of the adaptive disturbance compensation filter. A methodology for designing adaptive feedback noise cancelers in the presence of large model uncertainties is proposed. In addition to the overparametrization, a specific design of the linear feedback controller has to be done in order to satisfy a frequency condition in the range of variations of the frequencies characteristics of the compensatory path model. Experimental validation of the design is done on a relevant active noise control bench test.
- Bernard Vau, Ioan Doré Landau, « Adaptive rejection of narrow-band disturbances in the presence of plant uncertainties -A dual Youla-Kucera approach », Automatica (Elsevier), vol.129, July 2021. View
The stability of adaptive disturbance rejection schemes using Youla-Kucera (YK) parametrization and the internal model principle (IMP) in the presence of plant model uncertainties is investigated. The problem is approached by using the dual Youla Kucera parametrization for the description of the plant model uncertainties. The known disturbance case is discussed first emphasizing the need of over parametrization of the Youla Kucera filter used for control in order to both solving the IMP and the stability problems. Then this solution is extended for the case of unknown disturbances leading to the use of a parameter adaptation algorithm with projection. A stability analysis of the adaptive scheme is provided. Simulation results on relevant examples (including an active noise attenuation system) illustrate the possibilities of this approach for handling significant plant-model mismatch.
- Bernard Vau, Henri Bourlès, « Closed-loop output error identification algorithms with predictors based on generalized orthonormal transfer functions: Convergence conditions and bias distribution », Automatica (Elsevier), vol. 125, March 2021. View
This paper proposes an improved version of closed-loop output-error identification algorithms, where the predictor is established on a generalized basis of orthonormal transfer functions. It is shown that the selection of the basis poles impacts the convergence conditions and the bias distribution of the schemes.These algorithms present several advantages: They are able to identify in closed-loop fast sampled systems, stiff systems (with modes spread over three decades or more), and reduced order models. Moreover, they are suitable for unstable systems or controllers. A simulation example shows the effectiveness of this approach. These algorithms can be employed in an open-loop context by using a straightforward simplification.
- Bernard Vau, Henri Bourlès, « Some remarks on the bias distribution analysis of discrete-time identification algorithms based on pseudo-linear regressions », Systems and Control Letters (Elsevier), vol. 119, pp. 46-51, September 2018. View
In 1998, A. Karimi and I.D. Landau published in this journal an article entitled »Comparison of the closed-loop identication methods in terms of bias distribution ». One of its main purposes was to provide a bias distribution analysis in the frequency domain of closed-loop output error identication algorithms that had been recently developed. The expressions provided in that paper are only valid for prediction error identification methods (PEM), not for pseudo-linear regression (PLR) ones, for which we give the correct frequency domain bias analysis, both in open-and closed-loop. Although PLR was initially (and is still) considered as an approximation of PEM, we show that it gives better results at high frequencies.
- Bernard Vau, Henri Bourlès, « Generalized convergence conditions of the parameter adaptation algorithm in discrete-time recursive identification and adaptive control ». Automatica (Elsevier), vol. 92, pp. 109-114, June 2018. View
In this paper, we extend convergence conditions for the parameter adaptation algorithm, used in discrete-time recursive identification schemes, or in adaptive control. Whereas the classical stability analysis of this algorithm consists in checking the strictly real positiveness of an associated transfer function, we demonstrate that convergence can be obtained even when this condition is not fulfilled, under some assumptions on the algorithm forgetting factors. These results regarding both deterministic and stochastic contexts are obtained by analyzing convergence with a prescribed degree of stability.Top
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Ioan-Doré Landau, Tudor-Bogdan Airimitoaie, Bernard Vau, Gabriel Buche, « Can dynamic adaptation gain speed up recursive least-squares algorithm? ». 63rd Conference on Decision and Control (CDC), Milano (Italy), December 2024.
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Dynamic adaptation gain/learning rate have been introduced in the context of adaptation/learning algorithms using scalar adaptation gains/learning rates to accelerate the adaptation transients. This paper shows by means of theoretical analysis, simulations and, experimental results (on an active noise control system) that inserting a dynamic adaptation gain into the recursive least squares algorithm speeds up the adaptation transients in a deterministic environment and the asymptotic convergence in the stochastic case.
- Bernard Vau, Tudor-Bogdan Airimitoaie, « Recursive identification with regularization and on-line hyperparameters estimation ». 20th IFAC Symposium on system identification (SysId 2024), Boston (Massachusetts), July 2024. View
This paper presents a regularized recursive identification algorithm with simultane- ous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The performance of this novel scheme is compared with that of the recursive least squares algorithm in simulation.
- Bernard Vau, Henri Bourlès, «Generalized performance criteria for identified models». 20th IFAC Symposium on system identification (SysId 2024), Boston (Massachusetts), July 2024. View
Some misprints remain in the proceedings, please consult the corrected version available here: https://hal.science/hal-04654378/documentIt is shown that some usual criteria evaluating the performances of an identified model with respect to experimental data, like the FIT criterion, can be not well-suited to fast sampled systems. This leads to propose some generalized criteria where the signals are filtered by transfer functions belonging to an orthonormal basis. An interpretation of this filtering in the frequency domain is provided. The basis poles selection is equivalent to making a specification about the criterion in function of the expected use of the identified model.
- Tudor-Bogdan Airimitoaie, Bernard Vau, Dariusz Bismor, Gabriel Buche, Ioan-Doré Landau « Dynamic Variable Step Size LMS Adaptation Algorithms—Application to Adaptive Feedforward Noise Attenuation ». European Control Conference, Stockholm (Sweden), June 2024. View
The paper explores in detail the use of dynamic adaptation gain/step size (DAG) for improving the adaptation transient performance of variable step-size LMS (VS-LMS) adaptation algorithms. A generic form for the implementation of the DAG within the VS-LMS algorithms is provided. Criteria for the selection of the coefficients of the DAG filter which is required to be a strictly positive real transfer operator are given. The potential of the VS-LMS adaptation algorithms using a DAG is then illustrated by experimental results obtained on a relevant adaptive active noise attenuation system.
- Bernard Vau, Mehdi Bussutil, Colin Stevens, Romain Daudigny « On the optimal measurement time in north-finding procedures using maytagging ». IEEE Inertial Symposium, Hiroshima (Japan), March 2024. View
This article deals with gyro-based north-finding by using the maytagging approach. One proposes an analysis of the maytagging effect on the variance of the estimated azimuth, in function of the gyro disturbances (bias and noise). It is shown that it is preferable to impose a reduced time duration of the maytagging sequences, and to multiply the number of these sequences.
- Ioan Doré Landau, Tudor-Bogdan Airimitoaie, Bernard Vau, Gabriel Buche « Improving Adaptation/learning Transients Using a Dynamic Adaptation Gain/learning Rate — Theoretical and Experimental Results ». European Control Conference, Bucharest (Romania), June 2023. View
The paper explores in detail the use of dynamic adaptation gain/learning rate (DAG) for improving the performance of gradient type adaptation/learning algorithms. The DAG is an ARMA (poles-zeros) filter embedded in the gradient type adaptation/learning algorithms and generalizes the various improved gradient algorithms available in the literature. After presenting the DAG algorithm and its relation with other algorithms, its design is developed. Strictly Positive Real (SPR) conditions play an important role in the design of the DAG. Then the stability issues for adaptive/learning systems using a DAG are discussed for large and low values of the adaptation gains/learning rate. The potential of the DAG is then illustrated by experimental results obtained on a relevant adaptive active noise control system (ANC).
- Bernard Vau, Mehdi Bussutil, Nicolas Bernard « An Autonomous North Alignment Method for Motion Simulators ». IEEE Inertial Symposium, Kaua’i (Hawaii), March 2023. View
This paper proposes an autonomous method for the north alignment of a motion simulator. This method consists in employing Fiber Optic Gyros mounted on the platform of the turntable. The azimuth estimation is obtained by a specific maytagging procedure involving the two axes of the turntable. A mathematical model describing this method is provided and experimental results are also given: they show the interest of this approach.
- Ioan Doré Landau, Bernard Vau « Output Error Recursive Identification of Dual Youla-Kucera models in closed-loop operation ». European Control Conference, London (United Kingdom), July 2022. View
Dual Youla-Kucera plant model parametrization is very useful for describing model uncertainties. Therefore it is interesting to develop recursive identification algorithms for identification of these type of plant model structures in closed loop operation for potential use in iterative tuning or adaptive control. Closed loop output errors type recursive algorithms are developed specifically for this type of model structure. The algorithms assure global asymptotic stability in the deterministic environment and unbiased parameter estimation in the presence of noise when the plant model is in the model set. The algorithms will be applied for the identification in closed loop of a test bench for active noise control.
- Mehdi Bussutil, Bernard Vau, Damien Ponceau, Clément Pinzio, « Wobble estimation of a turntable axis by using an Inertial Measurement unit ». IEEE Inertial Symposium, Avignon (France), May 2022. View
A novel method for the characterization of axis wobble in a turntable (motion simulator) is proposed. The procedure relies upon data provided by gyros of an inertial navigation unit mounted on the machine. By eliminating the effects due to gyros biases, Earth rotation and gyros misalignment it is possible to compute the wobble effect as a function of the angular position of the turntable axis. Experimental results are displayed. They show that this method can advantageously replace the classical wobble measurement based on the use of inclinometers.
- Bernard Vau, Henri Bourlès, « A Pseudo-Linear Regression Algorithm in Discrete-Time for the Efficient Identification of Stiff Systems». 19th IFAC Symposium on system Identification (Sysid 2021), July 2021. View
This article presents a discrete-time identification algorithm able to characterize multiscale systems. It belongs to the pseudo-linear regression class, and uses a model parameterization established on generalized bases of orthonormal transfer functions. An analysis of the estimated parameters accuracy is provided, and in order to tend toward statistical efficiency, an iterative procedure of the basis poles selection is proposed. Simulation examples show the interest of the approach.
- Ioan Doré Landau, Bernard Vau, Gabriel Buche, « Adaptive Feedback Noise Attenuation in the Presence of Plant Uncertainties-A Dual Youla-Kucera Approach ». European Control Conference (ECC), June 2021. View
This paper presents an adaptive algorithm for the attenuation of tonal and narrow band noise in the case of large uncertainties of the compensatory path. This scheme implements the internal model principle for cancelling disturbances, combined with the Youla Kucera parametrization which allows to directly tune the disturbance compensation filter. The plant uncertainties are represented by means of the Dual-Youla-Kucera parameterization, and an overparametrization of the adaptive disturbance compensation filter is proposed to cope with the uncertain plant. In addition, a frequency condition has to be satisfied by an appropriate design of the central controller. The experimental validation of the design is done on a relevant active noise control test bench.
- Bernard Vau, Mehdi Bussutil, Joachin Honthaas, « A Testbench with Increased Accuracy for the Calibration of Inertial Navigation Systems and Inertial Sensors ». Institue of Navigation (ION), International Technical Meeting, January 2021. View
This paper presents a novel method to optimize the angular accuracy of the rotating tables (motion simulators) employed for the calibration of Inertial measurement units (IMU) and Inertial navigation Systems (INS). An example of an accelerometer calibration using such a table is given; it shows the role played by the table accuracy in the reliability of the calibration procedure. The motion simulator precision is mainly dependent on its angular encoder errors, which must be estimated in order to be compensated for. That leads to propose a novel method for the estimation of these encoder errors: this method provides a continuous estimation of the error over 360°, contrary to the existent procedure carried out by means of an interferometer along with a reflecting polygon fixed on the table axis. Some experimental results show the interest of the approach.
- Bernard Vau, Damien Ponceau, Mehdi Bussutil, « An embedded estimator for the self-diagnosis of a motion simulator ». Israël Navigation Workshop and Exhibition (INWE 20), Herzliya (Israël), January 2020.
- Bernard Vau, Ioan Doré Landau, « Youla-Kucera adaptive feedback disturbance rejection in the presence of plant uncertainties ». 58th IEEE Conference on Decision and Control (CDC 2019), Nice (France), December 2019. View
The stability of an adaptive disturbance rejection scheme based on the Youla-Kucera parameterization is investigated, in case of an uncertain plant model is used in the synthesis of the central controller. It is shown that stability is guaranteed provided that two conditions are satisfied at the same time: the first one is linked to the internal model principle, and the second one depends on the closed-loop poles location. For some uncertainties, these constraints cannot be met simultaneously with the minimal Q-filter. That leads to propose an over-parametrized Youla-Kucera filter, in order to relax the said conditions. Simulations on relevant examples illustrate the procedure for stabilizing the Youla-Kucera adaptive rejection scheme, in the presence of plant model uncertainties.
- Bernard Vau, Damien Ponceau, Mehdi Bussutil, « An improved control structure for the tracking of sine command in a motion simulator ». SPIE Optical metrology, Munich (Germany), June 2019. View
The evaluation of inertial sensor’s frequency response is a crucial step during the development of such sensors (gyroscope, accelerometer…). An accurate measurement of the sensor’s gain and phase requires a test equipment, usually a motion simulator, able to create accurately controlled motions over a wide frequency band, with minimum amplitude and phase uncertainty. State-of-the-art motion simulators use permanent magnet synchronous motors as actuators and optical encoders as angular position sensor. They also include a servo-loop whose bandwidth is necessarily limited either for theoretical reasons, like the Bode Integral Theorem, or for physical ones, such as the inevitable time-lags occurring in the loop, or even mechanical resonances. Nevertheless, the appropriate bandwidth is required to allow for an accurate inertial sensor characterization. A well-known way of coping with the intrinsic limitations of the feedback control structure in a servo-drive consists in introducing a specific filter (called feedforward) between the motion trajectory generator and the feedback loop, to provide an anticipation independently of the feedback structure. This compensation requires a good modelling of the controlled system transfer function but is never perfect. Moreover, in a motion simulator, the tested inertial equipment is subject to change, and a unique feedforward filter cannot provide an accurate enough compensation. Thus, iXblue has introduced an adaptive feedforward structure in the controllers of their motion simulators, leading to a more accurate tracking of sine commands, beyond the initial closed-loop bandwidth. The benefits of this control structure are quite significant: the sine tracking is very accurate, having very little amplitude attenuation and phase lag.
- Bernard Vau, Damien Ponceau, Mehdi Bussutil, « A control strategy for Coriolis and centrifugal effects reduction in an inertial test equipment ». 5th IEEE Inertial conference, Lake Como (Italy), March 2018. View
Modern systems for navigation, localization and guidance are increasingly making use of aiding data provided by additional non-inertial sensors. Test procedures for such hybrid systems often require simultaneous multi-axis motion simulators. It is crucial for this simulator to provide precise angular rate and positioning. However, this accuracy can be significantly affected by coupling between axes in case of multi-axis motion. This paper discusses how such coupling occurs and which methods may be implemented to mitigate the impact of this coupling in order to enhance the motion accuracy. The presented results demonstrate how an appropriate control strategy reduces drastically the coupling on rate and position stability, allowing for improved inertial systems testing.
- Bernard Vau, Henri Bourlès, « Laguerre based predictors in discrete-time recursive algorithms: A solution for open-loop identification under oversampling ». International federation of automatic control (IFAC), 20th world congress, July 2017. View
In this paper we propose a novel formulation of the predictor used in open-loop recursive identification algorithms. The predicted output is expressed by means of an orthogonal Laguerre transfer functions basis. This predictor representation presents many advantages: It makes it possible to identify robustly oversampled systems without any bias in low frequency, and to obtain relevant reduced order models. The Laguerre pole plays the role of a tuning parameter enabling the selection of the best approximation frequency area. The proposed schemes address both output error and ARMAX systems. Simulation and experimental results show all the practical benefits provided by these algorithms.
- Bernard Vau, Guillaume Baudet, « Narrow band attenuation by an ANC feedback algorithm based on Youla-Kucera parameterization ». Automotive NVH comfort, Société des ingénieurs de l’automobile (SIA), Le Mans (France), October 2016. View
Adaptive algorithms such as Fx-LMS remain hegemonic in the field of active noise control. However frequency varying narrow band noise rejection is now addressed more efficiently by linear feedback control techniques. In this paper we present all the advantages of a feedback algorithm based on the Youla-Kucera parameterization concept. This control algorithm, patented by IXBLUE, is very efficient for the rejection of multi-narrow bands such as booming noise in a car by following the engine speed, and also road noise in a specific frequency range. It exhibits very good robustness properties with respect to the variation of electro-acoustic transfer functions, due for example to the opening of a car windows. The structure of this algorithm is globally linear and all the tools of linear control science provide powerful means to tune the control system performances. Furthermore, the algorithm computing load remains very reasonable due to a significant lower sampling frequency compared to Fx-LMS. Extensive experiments carried out on several Renault vehicles demonstrate the suitability of this algorithm for the active noise control of car compartment.
- Bernard Vau, Philippe de Larminat, « Dry friction: Modelling and adaptive compensation ». 19th conference on system theory, control and computing (ICSTCC), Cheile Gradistei (Romania), October 2015. View
This paper presents an innovative dry friction model describing the Coulomb and Striebeck effects on a mechanical system. This model has the particularity of relying not only on the mechanical system velocity but also on its driving force. A compensation control structure providing feedback linearization is derived from the said model, with an additional adaptive control scheme guaranteeing efficient friction compensation in case of unknown or variant Coulomb parameter. Experiments carried out on a servo-system confirm the relevance of the proposed approach.
- Bernard Vau, « Improved multichannel attenuation of time-varying narrow band noise using Youla-Kucera parameterized filters -Algorithm and applications ». Internoise congress, Innsbrück (Austria), September 2013. View
Noise reduction in a vehicle compartment is a major issue that is increasingly achieved by active control techniques. In many applications, narrow bands disturbances are present (i.e. car booming noise, aircraft turboprop noise). This paper presents a novel multichannel feedback algorithm for attenuation of a narrow band noise that includes a linear time invariant (LTI) central controller interconnected with a Youla-Kucera infinite impulse response filter. Youla-Kucera filter gains are scheduled depending on noise frequency (that is supposed to be provided). Level of rejection and frequency wideness is easily tunable, and algorithm robustness with respect to uncertainty on the model of transfer functions between loudspeakers and error microphones can be easily assessed during a design stage. This is an important advantage compared to FXLMS or adaptive notch filter algorithms. Experimental tests performed on multichannel systems with two loudspeakers and two error microphones (in a configuration close to that of vehicle compartment) give excellent rejection performances for either fixed or varying noise frequency. Furthermore the robustness with respect to model uncertainty and low complexity of this approach makes this control law a good candidate for industrial implementation.
- Bernard Vau, « A novel algorithm for gyro-stabilization of Pan&Tilt motion platforms ». Symposium gyro, Karlsrühe (Germany), September 2011. View
This paper deals with gyro-stabilization of Pan & Tilt platforms supporting equipment such as cameras or antennas. These platforms aim to compensate for vehicle attitude variations, to keep a constant line of sight of the equipment. As the line of sight stabilization is performed by means of gyros, residual line of sight drift mainly depends on gyro biases. This presentation addresses an innovative stabilization algorithm: as the vehicle where the platform is mounted is generally equipped with an inertial measurement unit, it is possible to draw upon vehicle attitude information and combine it with platform gyro measurements and pan & tilt angular positions in order to estimate platform gyro biases. This estimation is performed by a Kalman filter. Estimated biases are then introduced in gyro control loops to reduce natural drift of the platform. This algorithm dramatically cuts down drifts induced by gyro biases and allows the use of tiny, low cost sensors (such as MEMS) without stabilization performance deterioration, compared to classical pan and tilt platforms using low bias, bulky and expensive gyros.Top
Title: Identification algorithms based on pseudo-linear-regression with predictors parametrized on generalized bases of orthonormal transfer functions
This thesis was defended on November 8, 2019. ViewThis thesis deals with identification of linear time invariant systems described by discrete-time transfer functions. For a given order, contrary to identification methods minimizing explicitly the prediction error variance, algorithms based on pseudo-linear regression produce models with a bias distribution dependent on the predictor parametrization. This has been demonstrated by the innovating concept of equivalent prediction error, a signal in general non-measurable, whose variance is effectively minimized by the pseudo-linear regression.
In a second step, some revisited versions of recursive algorithms are proposed (Output Error, extended least squares, and their equivalents in closed-loop), whose predictors are expressed on generalized bases of transfer functions introduced by Heuberger et al. in the 1990s and 2000s. The selection of the basis poles is equivalent to define the reproducing kernel of the Hilbert space associated to these functions, and to impose how approximation is achieved by the algorithms. A particular expression of this reproducing kernel is employed to introduce an indicator of the basis poles effect on the model fit in the frequency domain. This indicator plays a great role from a heuristic point of view. At last, a validation test in accordance with these algorithms is proposed and whose statistical properties are given.
This set of algorithms provides to the user some simple tuning parameters (the basis poles) that can be selected in function of the implicit purpose assigned to the identification procedure. Obtaining reduced order models is made easier, while identification of stiff systems –impossible until now in discrete-time- becomes accessible.Top
- Bernard Vau, Mehdi Bussutil, « Method for estimating the azimuth of a motion simulator comprising at least two axes, in order to set it to north». August 2022.
- Romain Sorant, Mehdi Bussutil, Bernard Vau, «Climatic chamber having thermal regulation for motion simulators, and method for thermal regulation, and installation kit». July 2021.
- Bernard Vau, Damien Ponceau, «Characterization method of a motion simulator and suitable device ». December 2018.
- Bernard Vau, Lionel Minne, « Method for optimising the performance of a servo control system of a mechatronic system, and suitable device ». December 2017.
- Bernard Vau, Mehdi Bussutil, « Method and device for compensation of Coriolis, centrifugal and gravity torques in a motion simulator ». June 2016.
- Bernard Vau, « Method and system for adaptive compensation of dry friction ». November 2014.
- Bernard Vau, « Method for active narrow band acoustic control, with variable transfer functions, and a corresponding system ». February 2013.
- Bernard Vau, « Method for the active acoustic control of narrow-band disturbing noise with one or more mobile microphones and corresponding system ». December 2012.
- Bernard Vau, « System for stabilizing a positioner with motorized axes of an item of equipment, method and application ». April 2011.
- Bernard Vau, « Method and device for active control of mechanical vibrations by the implemention of a control law consisting in a central controller and a Youla parameter ». November 2010.
- Bernard Vau, « Method and device for narrow band noise suppression in a vehicle passenger compartment ». May 2009.
- Bernard Vau, « Method and device for robust periodic disturbances rejection in an axis position control loop ». May 2008.
- Bernard Vau, « Optimization of the frequency response of a movement simulator ». January 2007.
- Bernard Vau, « Device for automatically adjusting servo controls of a movement mechanical simulator and associated device ». June 2005.
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- Bernard Vau, Tudor-Bogdan Airimitoaie, « Recursive identification with regularization and on-line hyperparameters estimation ». 20th IFAC Symposium on system identification (SysId 2024), Boston (Massachusetts), July 2024. View
- Ioan Doré Landau, Bernard Vau, Tudor Bogdan Airimitoaie, Gabriel Buche, « Improving performance of adaptive feedforward noise attenuators using a dynamic adaptation gain », Journal of Sound and Vibration (Elsevier), vol.560, May 2023. View