A New Uniformly Ultimate Boundedness Criterion for Temperature Dependent Average Bristle Deflections

Temperature variation intensively affects parameters of the friction force, particularly the average bristle deflections. In our earlier research work, a temperature dependent friction compensation scheme was developed for serial rigid robot manipulators which was comprised of a temperature dependent viscous friction compensation scheme and a temperature dependent disturbance rejection scheme. In this paper, a new criterion for the uniformly ultimate boundedness of the temperature dependent average bristle deflections is proposed in such a way that the temperature dependent average bristle deflections preserve the property of uniformly ultimately boundedness in a larger region. This is an improvement to our earlier research work. As the result of this improvement, it is shown that the proposed method in our earlier work, is applicable to larger temperature dependent disturbance terms. These two improvements are the main contributions of this paper that augment our earlier research work. The idea is supported by a new theorem.

Keywords:

Average bristle deflections , Friction compensation , Invariant set theory , Temperature dependent friction , Uniformly ultimately boundedness