Contribució a la identificació de models LTI intervalars en el domini de la freqüència
(English) The main objective of this Thesis is to provide an algorithm for the robust identification of models in the form of a transfer function with interval parameters. The starting uncertain data are in the frequency domain; its representation will consist of bands of uncertainty, polygons or ot...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | catalán |
| OAI Identifier: | oai:upcommons.upc.edu:2117/456028 |
| Acceso en línea: | https://hdl.handle.net/2117/456028 https://dx.doi.org/10.5821/dissertation-2117-456028 |
| Access Level: | acceso abierto |
| Palabra clave: | incertesa identificació robusta estabilitat robusta consistència (set-membership) pitjor cas (worst-case) incertidumbre identificación robusta estabilidad robusta consistencia (set-membership) peor caso (worst-case) uncertainty robust identification robust stability consistency (set-membership) worst-case 68 - Indústries oficis i comerç d'articles acabats. Tecnologia cibernètica i automàtica Àrees temàtiques de la UPC::Informàtica |
| Sumario: | (English) The main objective of this Thesis is to provide an algorithm for the robust identification of models in the form of a transfer function with interval parameters. The starting uncertain data are in the frequency domain; its representation will consist of bands of uncertainty, polygons or other flat figures in the complex plane. To reach the main objective of the work, firstly an extensive analysis of the mathematical tools and the characteristic measures of the candidate signals to excite the process is made. Different alternatives are studied to conveniently excite a process and it is verified that, whenever possible, it is necessary to apply band-limited harmonic signals to obtain information rich in spectral content. Thus, the model obtained will be able to represent the plant's behavior as faithfully as possible. Before proceeding to the robust identification itself, a historical review of nominal identification techniques is carried out. Emphasis is placed on the approach in the form of regressor of the problem. The approximation of the time delay of the plant and a method to decide the most suitable order for the model to be identified are studied. Given the inadequacy of the nominal model when looking at the data, it is proposed to incorporate uncertainty about the identified model in the form of interval parameters. The entire robustness study of the model pivots around Kharitonov's theorem, which assumes independence between the parameters of the polynomials. A chapter is dedicated to determining the frequency response of a transfer function with interval parameters based on this theorem. Within the algorithms proposed for robust identification, the work begins by extending the linear approach in parameters in the case of intervals. But this way of approaching the problem, despite presenting guarantees of convergence and optimality, shows an important fault when considering the frequency response of the identified model: it turns out to be insufficient to guarantee the inclusion of all observed data, since it omits part of the response when it establishes the restrictions of the problem. For this reason it is necessary to reformulate the problem as a non-linear optimization problem. The approach will have as its objective function to obtain the parameters of the model with the least dilation possible and that the response of the model adjusts in the most adapted way possible to the uncertain source data. The constraints will consider the property of inclusion of the data on the part of the model or vice versa. But these restrictions are given in the form of rules or in the form of a nested optimization problem. It is for this reason that it is necessary to properly condition the problem from the beginning. Since it is a non-convex optimization problem, without guarantee of a solution even though the appropriate order of the model is guessed, a previous study of stability and sensitivity is made to provide a seed and limits of the intervals to be found that ease to get the best possible solution. Throughout the Thesis there are application examples, synthetic and experimental, that show the wide scope of the proposed method and the diversity of plants on which it is applied. The thesis covers only linear, continuous and time-invariant (LTI) models. A future investigation would be to extend the results of this Thesis to the linear case with variable parameters (LPV). This would allow to put the interval coefficients of the polynomials of the identified transfer function as a function of one or several parameters that depend, for example, on the operating point of the plant. To avoid the inconvenience of the jumps caused by the restrictions in the form of rules in the optimization problem raised, it is proposed, as future work, to translate the rules as propositional logic. |
|---|