Page 83 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 5

RISE Based Asymptotic Prescribed

Performance Control of Servo

Systems With Continuously

Differentiable Friction Model

5.1 INTRODUCTION

As stated in previous chapters, adaptive control with function approxima-
tors such as neural network (NN) [1,2], fuzzy logic system (FLS) [3–5]has
been developed for servo systems with uncertainties and frictions. How-
ever, it is well known that most of function approximation based control
schemes can only guarantee the semi-global uniform ultimate boundedness
(SGUUB) of the controlled system due to the presence of unavoidable ap-
proximation errors. To address this issue, sliding mode control (SMC) [6]
has been used to eliminate the effect of the NN errors, which suffers from
chattering issue. Recently, a novel robust integral of the sign of the error
(RISE) control was developed in [7] to compensate for bounded uncer-
tainties and disturbances. The RISE based control designs can guarantee
asymptotic convergence by using a continuous integral of the sign of the
error feedback term, without the chattering. This technique was used in [8]
for an electrical motor with friction compensation. Recently, the idea of
RISE has also been incorporated into the adaptive neural network con-
trol for non-linear systems [9–12]. Although the RISE control strategies
can prove asymptotic convergence in the steady-state, there is no guarantee
for the transient convergence performance. In particular, when the func-
tion approximators with online learning are incorporated into the control
design, the potential sluggish response and large overshoot may create dif-
ficulties in the implementation.
On the other hand, the recently proposed prescribed performance con-
trol (PPC) [13,14] can guarantee and prescribe both the transient and
steady-state response, i.e., it can quantitatively characterize the convergence
rate, maximum overshoot, and steady-error. Although the PPC has been
successfully extended for various systems [15–17], the steady-state control
error of conventional PPF control (e.g., [13–16,18]) can only be retained
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00007-6 75
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