Page 66 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 4

Adaptive Prescribed Performance

Control of Servo Systems With

Continuously Differentiable

Friction Model

4.1 INTRODUCTION

In modern engineering applications, turntable servo systems are widely
used, where the presence of mechanical reduction and transmission devices
(e.g., gears, lead screws) connected to actuators may introduce significant
frictions [1]. To eliminate the effects of friction and achieve high preci-
sion motion control, some model-based compensation schemes have been
proposed [1–3]. However, the precise modeling of friction is challenging
since there are usually discontinuous dynamics in the classical friction mod-
els [4](werefertoChapter 1 for more details), so that time-consuming
offline identification should be conducted to determine all model param-
eters. Moreover, the fixed friction coefficients may not be able to account
for time-varying friction dynamics over a wide operation range.
To accommodate time-varying dynamics, adaptive control [5] has been
proved to be a powerful methodology for servo systems [6]. Furthermore,
to handle unknown non-linearities, neural networks (NNs) and fuzzy logic
systems (FLSs) have been also used [7–12]. In these schemes, the friction
is taken as a part of unknown non-linearities to be approximated, and thus
precise friction modeling is avoided. However, the NN weight to be up-
dated is a vector or matrix depending on the number of neurons such that
the subsequent computational costs may be demanding. Moreover, in these
adaptive control methods, the transient tracking performance cannot be
quantitatively studied and/or prescribed designed, which may limit their
practical application. Recently, an attempt to establish a priori specified per-
formance control paradigm has been reported [13,14], where the maximum
overshoot, the convergence rate, and steady-state error are all addressed.
In this chapter, we will propose an adaptive neural control for non-
linear servo systems with prescribed transient and steady-state tracking
performance. Inspired by [13]and [14], an improved prescribed perfor-
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00006-4 57
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