Discrete-time linear parametric identification: An algebraic approach

An improved and extended version is available at http://hal.inria.fr/inria-00188435/en/An algebraic framework for continuous-time linear systems identification introduced in the literature some years ago has revealed as an interesting alternative way for on-line parameter identification. The present contribution aims at conveying those ideas to linear time-invariant discrete-time systems, with particular emphasis attached to application issues. To this end, an on-line linear identifier for n-th order systems is evolved, re-sorting to the operational representation of the dynamics. Being discussed on the basis of a fifth-ordermodel of a drive-train, the numerical condition of the obtained setting of the identifier is found to suffer significantly with decreasing sampling times. A setting not experiencing these numerical problems is finally introduced by means of a re-parametrization of the identifier via application of the bilinear Tustin transform. The already implemented computer programs, where computer algebra plays an important role, are available. Note added on November 17th, 2007.- An improved and extended version is available at http://hal.inria.fr/inria-00188435/fr

An introduction to algebraic discrete-time linear parametric identification with a concrete application

International audienceAn algebraic framework for continuous-time linear systems identification introduced in the literature some years ago has revealed as an interesting alternative way for on-line parametric identification. The present contribution aims at conveying those ideas to linear time-invariant discrete-time systems, with particular emphasis attached to application issues. To this end, an on-line linear identifier for n-th order systems is evolved, re-sorting to the operational representation of the dynamics. Being discussed on the basis of a fifth-order model of a drive-train, the numerical condition of the obtained setting of the identifier is found to suffer significantly with decreasing sampling times. A setting not experiencing these numerical problems is finally introduced by means of a re-parametrization of the identifier via application of the bilinear Tustin transform. The already implemented computer programs, where computer algebra plays an important role, are available

Nichtlineare Regelung mit einem Raspberry PI

Die kommerziell erhältlichen Automatisierungssysteme sind sehr kostspielig. Hinzu kommen meist Lizenzgebühren für Software zur Simulation und Automatisierung. In diesem Artikel wird die Lösung einer anspruchsvollen Automatisierungsaufgabe, die Balancierung eines Balles auf einem rotierenden Rad, durch offene Software und preiswerte Hardware beschrieben. Zum Einsatz kommen der Einplatinencomputer Raspberry PI, das offene Hardware-Automationssystem BIOE und offene Software.The commercially available automation systems are quite expensive. Additionally, there are license fees for the simulation and automation software. In this article a challenging automation task, namely balancing a ball on a spinning wheel, is solved solely by open source software and inexpensive hardware. The single-board-computer Raspberry PI, the open hardware automation system BIOE and open source software are employed.(VLID)340038