In this paper we introduce a bristle model for stick-slip friction. The friction force of the bristle model is generated by frictionless contact between a body and an infinite row of bristles. Each bristle is attached to the ground through a torsional spring so that, as the body moves, the bristles pivot and counteract its motion. We show that the bristle model exhibits stick-slip motion similar to that of the LuGre model. We then form a hybrid model by combining the LuGre and bristle models.
F riction is a dynamic phenomenon of widespread importance, and the associated literature is vast; overviews are given in [1]- [5]. Friction can be viewed as an emergent, macroscopic phenomenon arising from molecular interaction. Consequently, both physical (physics-based) and empirical (experimentbased) models have been studied [2], [6]- [14]. Estimation and control methods are available for applications involving friction [15]-[18]; however, these topics are beyond the scope of this article.Friction models distinguish between presliding friction and sliding friction. Presliding or micro-slip friction refers to the friction forces that occur when the relative displacement between two contacting surfaces is microscopic, that is, on the order of the asperities (roughness features) on the surfaces. Sliding friction refers to the friction forces that arise when the relative displacement is macroscopic. Understanding presliding friction is useful for high precision motion control applications. For example, hysteresis can occur between the presliding friction force input and the displacement output [7], [11], [12].From a mathematical point of view, friction modeling is challenging since these models often involve nonsmooth dynamics. For example, the most widely used dry friction model, namely, Coulomb friction, is discontinuous. Additional discontinuous dry friction models are studied in [19]. Some friction models are continuous but have nonLipschitzian dynamics, which is a necessary condition for finite-settling-time behavior and the associated lack of time-reversibility [20], [21]. Table 1 classifies the properties of some widely used friction models.Hysteresis is the result of multistability, which refers to the existence of multiple attracting equilibria [22]-[24]. Multistability implies that hysteresis is a quasi-static phenomenon in the sense that the hysteresis map is the limit of a sequence of periodic dynamic input-output maps as the period of the input increases without bound. In both presliding and sliding friction models, there exist multiple equilibria corresponding to states that correspond to constant friction forces under constant displacement or velocity.In this article we examine several classical friction models from a hysteresis modeling point of view and study the
We apply retrospective cost adaptive control (RCAC) with auxiliary nonlinearities to a command-following problem for uncertain Hammerstein systems with rate-dependent hysteretic input nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. To account for the hysteretic input nonlinearity, RCAC uses auxiliary nonlinearities that reflect the monotonicity properties of the input nonlinearity. The hysteresis nonlinearity is modeled using the rate-dependent Prandtl-Ishlinskii model.
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