  This paper proposes a global iterative sliding mode control approach for
high-precision contouring tasks of a flexure-linked biaxial gantry system. For
such high-precision contouring tasks, it is the typical situation that the
involved multi-axis cooperation is one of the most challenging problems. As
also would be inevitably encountered, various factors render the multi-axis
cooperation rather difficult; such as the strong coupling (which naturally
brings nonlinearity) between different axes due to its mechanical structure,
the backlash and deadzone caused by the friction, and the difficulties in
system identification, etc. To overcome the above-mentioned issues, this work
investigates an intelligent model-free contouring control method for such a
multi-axis motion stage. Essentially in the methodology developed here, it is
firstly ensured that all the coupling, friction, nonlinearity, and disturbance
(regarded as uncertain dynamics in each axis) are suitably posed as
`uncertainties'. Then, a varying-gain sliding mode control method is proposed
to adaptively compensate for the matched unknown dynamics in the time domain,
while an iterative learning law is applied to suppress the undesirable effects
(arising from the repetitive matched and unmatched uncertainties in the
iteration domain). With this approach, the chattering that typically results
from the overestimated control gains in the sliding mode control is thus
suppressed during the iterations. To analyze the contouring performance and
show the improved outcomes, rigorous proof is furnished on both the stability
in the time domain and the convergence in the iteration domain; and the
real-time experiments also illustrate that the requirements of precision motion
control towards high-speed and complex-curvature references can be satisfied
using the proposed method, without prior knowledge of the boundary to the
unknown dynamics.
