Identification of Systems with Friction via Distributions using the Modified Friction LuGre Model

This paper presents the identification procedures based on distributions theory to continuous time systems with friction using the modified LuGre friction model. Mainly it applies the results of the identification procedures based on distributions theory to continuous time systems with friction. There are defined the so called generalized friction dynamic systems (GFDS) as a closed loop structure around a smooth system with discontinuous feedback loops representing friction reaction vectors. Both GFDS with static friction models (SFM) and dynamic friction models (DFM), also the modified friction LuGre model is analyzed. 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 advantage of representing information by distributions are pointed out when special evolutions as sliding mode, or limit cycle can appear.The proposed method is a batch on-line identification because identification results are obtained during the system evolution after some time intervals but not in any time moment. This method does not require the derivatives of measured signals for its implementation. Some experimental results are presented to illuminate its advantages and practical use.