Page 256 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 17

Identification and Inverse Model

Based Control of Uncertain

Systems With Backlash

17.1 INTRODUCTION

The backlash behavior exists widely in the electromagnetic relay circuit,
high precision servo systems and robotic systems, which makes them non-
smooth, non-linear systems. The non-smooth and non-linear dynamics are
mainly due to its memory and multi-value mapping property, which can
be taken as a specific hysteresis [1]. The existence of the backlash in the
control systems can result in tracking error, limit-cycles, and even lead to
system instability.
To address such non-linear dynamics, conventional methods were pro-
posed based on the idea of inverse compensation, where the inverse model
of hysteresis is connected in a cascaded manner to the output of con-
troller [2]. This leads to many adaptive inverse compensation control
methods for both continuous-time and discrete-time systems [2–4]. An
adaptive robust control (ARC) was also proposed [5], which takes the
unknown backlash characteristics as the parameterized linear system, and
introduces a robust term to compensate the modeling error. In [6], two
adaptive backstepping controllers have been proposed for systems with un-
known backlash-like hysteresis. However, these methods require that accu-
rate backlash model should be known in a priori, requiring possible offline,
time-consuming identification procedure, which is not a trivial task due to
the non-smooth property in the conventional backlash models. To relax the
requirements of offline modeling, several intelligent control schemes have
been also reported, where neural networks [7] and fuzzy logic systems [8]
are used in the feedback control system.
In this chapter, a robust inverse model based compensation control is
presented for Hammerstein systems in presence of input asymmetric back-
lash non-linearities, where a new dynamic model for backlash inverse is
suggested. The piecewise linear parametric representation is first utilized
to simultaneously estimate the characteristic parameters of the backlash
and the unknown coefficients in the linear transfer function. Then a ro-
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00022-2 257
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