Page 12 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

PART 1

Introduction

The existence of non-smooth behaviors (e.g., friction, dead-zone, satura-
tion, and hysteresis) in the control systems may deteriorate the performance
severely, which in turn leads to difficulties and challenges in the control
design and implementation. Classical methods to accommodate such non-
smooth dynamics are based on the idea of inverse model compensation.
This method presumes that offline modeling and identification should be
conducted, which is not a trivial task. On the other hand, adaptive control
has been proved to be a promising control design technique for systems with
uncertain parameters, where the model and/or control parameters can be
online adjusted by using the information on the systems operation. Hence,
it is of interest to exploit adaptive schemes to address the modeling and
control problems for uncertain systems subjected to the above mentioned
non-smooth dynamics.

1.1 PROLOGUE

In practical industrial plants, actuator and sensor non-linearities are among
the key factors limiting both the static and dynamic performance of feed-
back control systems. Non-smooth non-linearities such as friction, dead-
zone, hysteresis, and saturation are usually unavoidable in such control sys-
tems due to the use of various actuators and sensors: mechanical, hydraulic,
pneumatic, magnetic, piezoelectric, etc. These “hard” non-linearities are
ubiquitous and can serve as aggregate representation of more complex
1