Page 273 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 18

Identification and Control of

Hammerstein Systems With

Hysteresis Non-linearity

18.1 INTRODUCTION

Hammerstein system is a typical non-linear system with a static non-
linearity (e.g., hysteresis, dead-zone, and backlash) and a linear dynamic
system connected in series. Thus, Hammerstein model can be used to de-
scribe many practical systems [1–6]. Fig. 18.1 illustrates the basic structure
of a Hammerstein system, where the input u(t) and output y(t) are measur-
able, whereas the output of the static non-linearity x(t) (also the input of
linear dynamics) is not available for measurement. Consequently, the iden-
tification of Hammerstein system is a challenging task [7–10]. Among pre-
viously mentioned identification methods, the blind identification reported
in [8] only requires the output measurements and thus makes the Hammer-
stein model identification possible without using the internal variable x(t).
Blind identification was originated from the blind channel equalization in
communications [11]. By using the over-sampling output, a single input
single output (SISO) system can be equivalently transformed into a single
input multiple output (SIMO) system [8,9,12]. In this respect, blind identi-
fication can identify the structure and the parameters of linear dynamics by
using over-sampling output measurements y(t) only. However, the Hystere-
sis non-linearities are not specially considered in all these aforementioned
identification results.
Hysteresis dynamics can be found in smart materials, physical systems,
and biological systems, for example, piezoelectric actuators, shape memory
alloys, and electromechanical systems [13–15,12]. The control design for
such systems usually requires precise hysteresis models to compensate for
its dynamics. In this respect, the identification of hysteresis dynamics has
attracted many attentions [12,16–18]. In particular, among different hys-
teresis models as reviewed in Chapter 16, the Preisach model of hysteresis
non-linearities has been widely used due to its simplicity in the identifica-
tion.
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00023-4 275
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