![](bg1.png)
Development of Robust Learning Control and Application
to Motion Control
Meng-Shiun Tsai, Chung-Liang Yen and Hong-Tzong Yau
Department of Mechnaical Engineering and Advanced, Institute of Manufacturing with High-tech Innovations,
National Chung-Cheng Unviersity, 168, University Rd, MinHsiung, Chiayi, Taiwan
Keywords: Iterative Learning Control, Motion Control, Nurbs Curves, Robust H
∞
Control.
Abstract: In this paper, the error dynamic equation of the ILC algorithm is derived with consideration of parameter
uncertainties and noise. The H
∞
frame work is utilized using the derived error dynamics to design the robust
learning controller. The proper learning gain is designed based on an optimization process to ensure that
both tracking performance and convergence condition can be achieved. Simulation and experiments are
conducted to validate the robust learning algorithm and the system is stable ever under high payload
uncertainty.
1 INTRODUCTION
Iterative learning control (ILC) is a technique to
control the system when it operate same tasks
repetitively. The ILC can be applied to robot
manipulators (Tayabi and Islam, 2006), chemical
batch process (Lee and Lee, 2007), and so on. Many
schemes of the ILC including the 2D theory method
(Geng et al., 1990), stochastic method (Wang and
Afshar, 2009), inverse system (Ye and Wang, 2005),
and feedback learning operators (Goldsmith, 2002;
Chin et al., 2004) have been proposed. Technical
review on the methodologies and applications of the
ILC is referred to (Ahn et al., 2007).
System robustness is generally a major concern
in the implementation of ILC to either linear or
nonlinear systems. The adaptive iterative learning
control was proposed (French and Rogers, 2000).
The Lyapunov method was adopted to prove the
convergence of the algorithm. Other adaptive ILC
algorithms were proposed to handle system with
time-varying parameters using a positive-definite
Lyapunov-like sequence (Kuc et al., 1991). Another
approach to ensure system robustness is to utilize the
H
∞
theory to formulate the general design
framework for the ILC algorithm (Padieu and Su,
1990). In these papers, only the performance and
robustness analysis of ILC schemes are considered.
In this paper, two steps design process is
proposed. The first step is to design the H∞
controller without consideration of the system
uncertainty. But the noise effect is included in the
design process. The second step is to iterate the
learning gain such that the convergence condition is
satisfied even under large system uncertainty. The
learning gain served as the performance weighting
which is the loop optimization variable to further
minimize system performance. Simulations and
experiments are conducted to demonstrate the design
philosophy.
2 MODELLING OF SERVO
CONTROL SYSTEM
In this paper, the command-based ILC is applied to a
CNC milling machine tool (Tsai et al., 2006). The
general servo control system as shown in Fig. 1
which includes the linear dynamic model of the
servo system, the velocity and position loops with a
velocity feedforward controller F(s). The function
)s(F
is designed as
sK
f
where
f
K
is the
feedforward gain. The J
s
, B
s
, K
t
and h
p
are the
moment of inertia, viscosity, torque constant and
pitch of lead screw. The parameters
vp
K
and
vi
K
in
the velocity loop can be designed by specifying the
damping ratio and bandwidth of the closed-loop
transfer function of the velocity loop. The position
gain
pp
K
in the position loop is determined by the
designed bandwidth of the position loop. The
148
Tsai M., Yen C. and Yau H..
Development of Robust Learning Control and Application to Motion Control.
DOI: 10.5220/0004008601480152
In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2012), pages 148-152
ISBN: 978-989-8565-21-1
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)