Page 28 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 2

Adaptive Sliding Mode Control of

Non-linear Servo Systems With

LuGre Friction Model

2.1 INTRODUCTION
Mechanical servo systems have been widely used in industrial robots,
electronic processing, laser processing equipments, and manufacturing ma-
chines,etc.[1]. In such servo systems, the existence of non-smooth non-
linear characteristics, such as friction, dead-zone, and hysteresis, may affect
the tracking accuracy and even lead to the instability [2–4]. Among these
non-smooth non-linearities, friction can cause steady-state tracking errors,
limit cycle oscillations, and even low velocity crawlings. Therefore, it needs
specific considerations to reduce or eliminate the effect of frictions in the
control design. As one of the most widely used friction models, LuGre
model is able to describe most of friction characteristics including Stribeck
effect, pre-sliding, and static friction as stated in Chapter 1.However, the
identification of parameters in this model is generally difficult because some
parameters are in a non-parameterized form, such that the deterministic
system identification (e.g., gradient or least squares) algorithms are not di-
rectly applicable.
Recently, some advanced intelligent identification methods have been
proposed, such as genetic algorithm (GA), ant colony optimization
(ACO), particle swarm optimization (PSO), glowworm swarm optimiza-
tion (GSO), and so on [5–7]. Among those identification algorithms, GSO
requires less prior knowledge and has high computational efficiency [8,9]
and thus is suitable for friction parameter identification. On the other hand,
to compensate for the effect of frictions, both model-free compensation and
model-based compensation schemes have been developed, including PID
control, neural network control, fuzzy control, adaptive control [10–14].
Specifically, the model-based compensation scheme can be derived based
on the identified friction models, and thus is easily incorporated into vari-
ous control designs.
In this chapter, we propose an adaptive non-linear siding mode control
for mechanical servo systems based on glowworm swarm friction iden-
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00004-0 19
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