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Vol: 51(65) No: 2 / June 2006        

On the Generalized Friction Dynamic Systems Identification by Distributions
Constantin Marin
Department of Automation, University of Craiova, Faculty of Automation, Computers and Electronics, Bd. Decebal, no. 5, 200440 Craiova, Romania, phone: +40.251.438198, e-mail: cmarin@automation.ucv.ro
Anca Petrisor
Department of Electromechanics, University of Craiova, Faculty of Electromechanics, Bd. Decebal, no. 5, 200440 Craiova, Romania, phone: +40.251.438198, e-mail: aperisorn@em.ucv.ro
Virginia Finca
Department of Electromechanics, University of Craiova, Faculty of Electromechanics, Bd. Decebal, no. 5, 200440 Craiova, Romania, phone: +40.251.438198


Keywords: identification, distribution theory, friction.

Abstract
A class of nonlinear systems is represented by smooth systems with discontinuous feedback loops depending on both the state and input vectors called generalized friction dynamic systems (GFDS) as they have been presented for the first time in [17]. The feedback loops generate some reaction vectors assimilated to friction vectors from mechanics. This paper extends some aspects of the above approach regarding identification procedures based on distributions theory to GFDS. Both GFDS with static friction models (SFM) and dynamic friction models (DFM) are considered. The identification problem is formulated as a condition of vanishing the existence relation of the system. Then, this relation is represented by functionals using techniques from distribution theory based on testing function from a finite dimensional fundamental space. The proposed method in [17] is a batch on-line identification method because identification results are obtained during the system evolution after some time intervals but not in any time moment. Even if it is based on the input-output measurements only, the method is insensitive to the initial state of any transient. In this paper, the identificability conditions and the sticky surface are presented in detail. The advantages of representing information by distributions are pointed out when special evolutions as sliding mode, or limit cycle can appear. The proposed method does not require the derivatives of measured signals for its implementation. Some experimental results are presented to illuminate further its advantages and practical use.

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