Page 20 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 1

Friction Dynamics and Modeling

1.1 INTRODUCTION

Friction appears in most of mechanical systems, where there is motion or
tendency for motion between two physical components because all surfaces
are irregular at the microscopic level. The existence of friction could cause
a steady-state error, a limit cycle, or stick-slip phenomenon at low speed
in the motion control systems. As a result, it is of great interests for engi-
neers to understand the behaviors of frictions and then design appropriate
controllers to eliminate the undesirable effect of friction. In fact, friction
modeling and compensation have attracted a significant interest in the con-
trol community.
In order to achieve high-performance control, friction dynamics need
to be precisely described. Unfortunately, since friction behavior is affected
by many factors such as velocity, temperature and lubrication, develop-
ing accurate friction models has been a long-standing problem, which has
not been fully solved [1]. In particular, owing to the high non-linearity
and non-smooth property, it is generally difficult to build a unified, sim-
ple mathematic friction model, which can cover most friction dynamics,
such as Static friction, Coulomb friction and Viscous friction, etc. Several
classical friction models with different components (e.g., Static friction,
Coulomb friction, Viscous friction and Stribeck effect) have been devel-
oped in the literature [2]. Apart from static frictions, some dynamic friction
behaviors (e.g., presliding displacement, friction lag and stick-slip motion)
have been also considered in these models. Among these dynamic mod-
els, LuGre model (a dynamic model) has been widely used in the model
based compensation schemes [3] since this model can cover most of fric-
tion behaviors. Modified LuGre models have been further investigated and
incorporated into the control designs to eliminate the effectiveness of fric-
tions [4,5].
It is noted that these classical models are generally discontinuous or
piecewise continuous, making the identification of model parameters and
the model based control implementation difficult. To facilitate control de-
signs, continuousness of friction models is also an important aspect to
be considered. In [6], a continuously differentiable friction model was
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00003-9 11
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