Page 114 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 7

Dead-Zone Dynamics and

Modeling

7.1 INTRODUCTION
Systems with hard input non-linearities are ubiquitous in various electrical
and mechatronics devices such as ultrasonic motors, servo valves, smart ac-
tuators, and sensors. Among those hard non-linearities, dead-zone is one of
the most commonly encountered non-smooth non-linearities, in particular
in recently developed smart actuators [1,2]. The dead-zone input non-
linearity is a non-differentiable function that characterizes a non-sensitivity
for small excitation inputs. Therefore, as reported in the literature, the pres-
ence of dead-zone in the control systems could severely limit the system
performance. This obviously creates inherent difficulties in the control de-
signs.
To handle the dead-zone input in the actuators, traditional control
schemes are based on the inverse dead-zone compensation (see [1,3]and
the references therein), where the inverse of the dead-zone dynamics is
added/connected in the controller output, such that the effect of dead-
zone in the actuator can be eliminated. To achieve this purpose, accurate
dynamics of dead-zone should be precisely modeled by using mathematical
formulations. Hence, a natural linear formulation of dead-zone was ini-
tially suggested and used in the control design [1]. Specifically, this linear
dead-zone model has been subsequently incorporated into adaptive con-
trol designs for linear and non-linear uncertain systems [4,3]. However,
some characteristic parameters, e.g., maximum and minimum values of
dead-zone slopes or width, are assumed to be precisely known. Hence,
as mentioned in [5], the identification of dead-zone model is not triv-
ial since the intermediate variables used for the identification may not be
measured directly. Recently, some new control designs without using dead-
zone inverse were also reported. A robust adaptive control was developed
for a class of non-linear systems without constructing the inverse of the
dead-zone [6], where the dead-zone input non-linearity is modeled as a
combination of a linear system plus a disturbance-like term. However, this
method is only suitable for systems with symmetric dead-zones input (i.e.,
a dead-zone with equal slopes). Extension of the results to non-symmetric
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00010-6 109
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