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Optimal identification experiment design : contributions to its robustification and to its use for dynamic network identification : resonance frequency tracking

Abstract : At the roots of every engineering field there are mathematical models. They allow us to make predictions on the evolution of a process, monitor the health of a plant and design a control scheme. System Identification provides us with techniques for obtaining such a model directly from experimental data collected from the system we want to model, leading to a model which is accurate enough. In order to obtain a good model using the tools of System Identification, a user has to choose: a model structure, the experimental data and an estimation method.The choice of the experimental data relies on designing the experiment and it has important consequences on the final quality of the model. Indeed, if we consider the identification of a model among a set of transfer functions (model structure) in the Prediction Error framework, the “larger” the power spectrum of the excitation signal, the more accurate the model. On the other hand, a “large” power spectrum for the excitation signal represents a high cost for the experiment. In this context, the least-costly experiment design framework has been proposed, where the cost is minimized while requiring a model which is just accurate enough.In all optimal experiment design problems, the underlying optimisation problem depends on the unknown true system that we want to identify. This problem is generally circumvented by replacing the true system by an initial estimate. One important consequence of this approach is that we can underestimate the actual cost of the experiment and that the accuracy of the identified model can be lower than desired. Many efforts have been done in the literature to make this optimisation problem robust, leading to the research area of robust optimal experiment design. However, except for simple cases, all the approaches proposed so far do not completely robustify the optimisation problem. In this thesis, based on an a-priori uncertainty set for the true system, we propose a convex optimization approach that guarantees that the experiment cost will not be higher than a computed upper bound and that the accuracy of the model is at least the desired one. We do this considering that the excitation signal is a multisine signal.In recent years we have observed in control engineering a rising interest in networks. Even if many Identification problems in the network context have been recently studied, this is not the case for the optimal experiment design. In this thesis, we consider the optimal experiment design for the identification of one module in a given network of locally controlled systems. The identification experiment will be designed in such a way that we obtain a sufficiently accurate model of the to-be-identified module with the smallest identification cost i.e. with the least perturbation of the network.Finally, in the second part of this thesis we consider the drive mass system of MEMS gyroscope. This drive mass system is meant to oscillate at its resonance frequency in order to have the desired performances. However, during its operation the gyroscope undergoes environmental changes, such as temperature changes, that affect the resonance frequency of the resonator. It is then important to track these changes during the operation of the gyroscope. To do so, in this thesis, we investigate two solutions: one coming from adaptive control, the extremum seeking scheme, and one coming from System Identification, the recursive least squares algorithm.
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Submitted on : Tuesday, June 22, 2021 - 6:28:09 PM
Last modification on : Thursday, September 1, 2022 - 11:05:19 AM
Long-term archiving on: : Thursday, September 23, 2021 - 7:18:44 PM


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  • HAL Id : tel-03267982, version 1


Federico Morelli. Optimal identification experiment design : contributions to its robustification and to its use for dynamic network identification : resonance frequency tracking. Other. Université de Lyon, 2021. English. ⟨NNT : 2021LYSEC002⟩. ⟨tel-03267982⟩



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