Page 216 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 14

Non-singular Terminal Sliding

Mode Funnel Control of Servo

Systems With Input Saturation

14.1 INTRODUCTION

Over the past decades, servo systems driven by motors have been widely
used in practical applications [1]. The mechanical connection between the
servo motors and manipulation devices produces non-smooth non-linear
dynamics on their outputs and/or inputs such as saturation, hysteresis,
dead-zone, and so on. During the operation, the violation of the input
constraints may lead to performance degradation or even system damage.
Consequently, it is a challenging task for control designs of motor servo sys-
tems. As one of the most important non-smooth non-linearities, saturation
implies that the magnitude of the control signal has certain constraints [2].
Apart from the well-known anti-windup scheme, many significant re-
sults on adaptive control for systems with input saturation have been
recently obtained [3–5]. However, the lower and upper bounds of the sat-
uration constraints should be exactly known or estimated in the control
design. In [6]and [7], adaptive control design have been investigated with-
out using the exact knowledge of saturation bounds.
On the other hand, to retain the output or error constraint, several
effective techniques have been investigated, such as barrier Lyapunov func-
tion [8–10], prescribed performance control (PPC) [11,12] and funnel
control [13,14]. As an almost non-model-based control technique, fun-
nel control could guarantee that the output error can be strictly guaranteed
within a given bound. In [15], a funnel dynamic surface control with pre-
scribed performance was further proposed. However, the steady-state error
may not converge to zero in finite time.
In this chapter, a non-singular terminal sliding mode funnel control
is developed to achieve a prescribed tracking performance for uncertain
servo systems with unknown input saturation. A smooth and affine func-
tion is used to approximate the input saturation dynamics. To avoid using
the complex barrier Lyapunov function or inverse transformed function in
the PPC, a funnel constraint variable is utilized in constructing the non-
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00018-0 215
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