Identificación de un Sistema de Fijación de Tornillos con Ruido en Mediciones
Identification of a Screw Fastener System with Noises in Measurements
Raúl Ramírez López1 y Roberto Salas Zúñiga2
1 Instituto Tecnológico de Querétaro Av. Tecnológico S/N, esq. Gral. Mariano Escobedo, Centro Histórico. 76000 Querétaro, Qro.
e–mail: raulramirezlopez@bigfoot.com
Artículo recibido en Junio 06, 2005; aceptado en Septiembre 11, 2006
Resumen
La identificación de sistemas es una tarea anterior fundamental al control de los mismos. El estado del arte en la identificación ha permitido resolver el problema de conocer el modelo de los sistemas con alta precisión, considerando que las mediciones de las variables del sistema son realizadas sin error; o bien, efectuando algún tratamiento de filtrado. Sin embargo, existen casos donde habiendo ruido en las mediciones, este filtrado no es posible, o donde los errores son atribuibles a la modelación. Muchos de los esfuerzos hechos para resolver este problema giran alrededor de la idea de disminuir los efectos del ruido sobre las señales de interés, para después despreciar el ruido residual. Pero existen aplicaciones donde aún después de disminuir los efectos, es imposible ignorar su influencia. Como ejemplo se puede mencionar el caso de sistemas inestables, donde es necesario ejercer una acción de control mientras se efectúa la identificación, y la presencia de una señal de retroalimentación provoca polarización en los identificadores. En este trabajo, se presenta una solución al problema de identificación de sistemas con ruidos en mediciones, mediante una modificación al esquema de identificación clásico Mínimos Cuadrados Extendidos (ELS), llamada Mínimos Cuadrados Sobre–Extendidos (abreviado OELS del inglés), propuesta por el autor como tesis doctoral, es demostrada bajo ciertas condiciones y aplicada a la identificación de un sistema de fijación de tornillos, el cual está sometido constantemente a ruido en las mediciones, debido tanto a la forma de efectuar la medición, como a influencias electromagnéticas externas. Los resultados son obtenidos en simulación, pero están basados en datos directamente adquiridos del sistema atornillador, y muestran el adecuado desempeño del algoritmo OELS.
Palabras clave: Identificación, control, estocástico, ruido en mediciones, Mínimos Cuadrados Extendidos, ELS, Mínimos Cuadrados Sobre–Extendidos, OELS, atornilladora.
Abstract
]]> System identification is a fundamental previous task to system control. State of art in system identification has allowed to solve the problem of knowing the system model with high precision, considering that the system variables measurements are made without error; or making some filtering treatment. However, there are cases where, even there exist noises in measurements, the filtering treatment is not possible, or where errors are attributable to the model. Many of the efforts made to solve this problem are around of the idea of diminishing the noise effects over the interest signals, and then depreciate the residual noise. But there are applications where even after diminishing the effects is impossible to ignore its influence. As an example, it can be mentioned the case of unstable systems, where is necessary a control action while the identification is carried out, and the presence of a feedback signal leads to have biased estimators. In this work, a solution to the problem of system identification with measurement noises is presented, by means of a modification of classical identification Extended Least Squares scheme (ELS), called Over–Extended Least Squares (OELS), proposed by the author in his PhD thesis, it is proved under certain conditions and it is applied to identify a screw fastener system, which is constantly submitted to measurement noises, as much by the form the measurement is made, as by external electromagnetic influences. Results are obtained in simulation, but are based on directly acquired data from the fastener system, and show the reliable performance of the OELS algorithm.Keywords: Identification, Control, stochastic, noises in measurements, noisy measurements, Least Square, Extended Least Square, Over–Extended Least Square, fastener system.
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Agradecimientos
El autor expresa su agradecimiento a los Ingenieros Gilberto Barroso Gil y Juan Carlos Palos, de la empresa Ejes Tractivos, S. A. de C. V., por su colaboración para la toma de datos de las atornilladoras Cooper, así como por su autorización para presentarlos en este artículo.
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