Page 100 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 6

Adaptive Control for

Manipulation Systems With

Discontinuous Piecewise

Parametric Friction Model

6.1 INTRODUCTION

Similar to servo systems studied in the previous chapters, the non-linear,
complex joint friction in the manipulator systems also affect the position
control accuracy, i.e., it can lead to tracking error, undesired stick-slip, and
limited cycles, particularly when the motion is with low velocities. Most of
available work on the modeling and compensation of frictions, e.g., [1,2],
can be roughly divided into two categories: model based and model-free
friction compensation.
In model based compensation, the effect of friction is compensated by
applying an equivalent control force in the opposite direction. Commonly
used friction models were developed by static maps between the velocity
and the friction force with fixed coefficients. Typical examples are dif-
ferent combinations of Coulomb friction, viscous friction, and Stribeck
effect [3]. Canudas et al. [4] proposed a dynamic LuGre model for some
typical servo systems, which can capture most of the friction behaviors in-
cluding Stribeck effect, hysteresis, and varying break-away force. We refer
to Chapter 1 for more details of different friction models. It is noted that
these friction models with fixed parameters may not be able to achieve sat-
isfactory performance at both low speed and high speed regions due to the
speed-dependant property of frictions. Moreover, there are many parame-
ters to be estimated in these models and some of them are not in the linearly
parameterized form; this fact makes the identification of these models quite
time-consuming and challenging [5].
On the other hand, the model-free methods have been mainly devel-
oped based on intelligent methods by using their non-linear approximation
and learning abilities, e.g., support vector machine (SVM) [6], fuzzy logic
systems [7], and Gaussian radial basis function network [8]. However, the
non-smooth characteristics of frictions make these approximations less ef-
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00008-8 93
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