Page 123 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 8

Adaptive Finite-Time Neural

Control of Servo Systems With

Non-linear Dead-Zone

8.1 INTRODUCTION
Over the past decades, permanent magnet synchronous motor (PMSM) has
been widely studied in motion control applications [1–3]. The mechan-
ical connection between servo motors and mechanical devices produces
non-smooth non-linear characteristics such as dead-zone, friction, back-
lash, and hysteresis [4–7], etc. As one of the most important non-smooth
non-linearities in the servo systems, the dead-zone may lead to severe per-
formance deterioration or even instability [8]. To handle the systems with
unknown dead-zones, much research has been carried out [9–15].
Among different control methodologies, sliding mode control (SMC)
is regarded as one of the robust control techniques to deal with system
uncertainties and disturbances. In particular, a new terminal sliding mode
control (TSMC) scheme has been recently developed to achieve the finite-
time stability [16–18], which has been developed based on the principle of
SMC, but with fast convergence. One of the critical issues in the TSMC
design is the potential singularity problem involved in the control imple-
mentation. To address this issue, several non-singular terminal sliding mode
control methods were also investigated in [19–21]. Although TSMC can
cope with bounded system uncertainties and external disturbances, the sys-
tem models in those aforementioned approaches are usually required to be
known or partially known, which may limit their applications for practical
PMSM servo system.
To address the unknown non-linearities and dead-zone dynamics, neu-
ral networks (NNs) have been successfully employed, where the system
uncertainties and unknown non-linearities can be online approximated
by using NNs in viewing their function approximation property [22–26].
Specifically, it is shown in [27] that the dead-zone dynamics can be approx-
imated via augmented NNs by introducing extra neurons whose activation
functions provide a “jump function basis set” for approximating piecewise
continuous functions. Moreover, the non-linear dead-zone in the system
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00011-8 119
Copyright © 2018 Elsevier Inc. All rights reserved.