Page 46 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 3

Adaptive Dynamic Surface

Control of Two-Inertia Systems

With LuGre Friction Model

3.1 INTRODUCTION
In some servo mechanisms, the driving motor is connected to a load
through a stiffness shaft and flexible coupling, which can be modeled as
a two-inertia system. This configuration may cause torsional vibrations,
which lead to failures of the drive system in some cases. In order to achieve
stable operation and satisfactory tracking response of the load, it is neces-
sary to address torsional vibrations in the control design. In some control
methods for such systems, e.g., [1–3], the system states such as motor speed,
shaft torque, load speed, and disturbance torque are used as feedback sig-
nals, which may be difficult to measure in reality. Thus, state observers
are needed to estimate these variables [4–8]. Moreover, some artificial in-
telligent techniques are also utilized for two-inertia systems, e.g., neural
networks [9], and neuro-fuzzy system [10], [11], [12].
To address the non-linear frictions and unknown dynamics in the con-
trol system, recurrent neural networks (RNNs) and fuzzy logic systems
(FLSs) have been used due to their non-linear approximation and learn-
ing abilities [13–18]. In particular, echo state networks (ESNs) have been
developed as simplified RNNs [19,20], which require a simpler training
procedure than other NNs, i.e., the training of ESNs does not need to ad-
just the weights between the input layer and the hidden layer. To further
address the potentially sluggish transient response (e.g., overshoot, con-
vergence rate) of classical adaptive control with function approximators,
a new prescribed performance control (PPC) approach was proposed [21],
where a prescribed performance function (PPF) is incorporated into con-
trol design to guarantee the convergence of tracking error to a predefined
arbitrarily small region, and the convergence rate no less than a predefined
value. The applications of this PPC to turntable servo system [22]and ve-
hicle suspension [23] have also been reported.
In this chapter, we incorporate an improved PPC [24]intoarecur-
sive dynamic surface control (DSC) design (an enhanced backstepping
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00005-2 37
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