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S. Ito, H. W. Yoo, G. Schitter:
"Comparison of Modeling-free Learning Control Algorithms for Galvanometer Scanner´s Periodic Motion";
Talk: IEEE/ASME International conference on advanced intelligent mechatronics AIM2017, Munich (Germany); 07-03-2017 - 07-07-2017; in: "AIM 2017 Proceedings", (2017), 6 pages.

For an accurate and precise periodic scanning
motion of a galvanometer scanner, this paper presents iterative
learning control (ILC) that is designed and implemented in the
frequency domain to compensate for system nonlinearities, such
as static friction. For a case that system identification in advance
is difficult due to the nonlinearities, the frequency-domain ILC
itself incorporates and performs system identification during
iterative learning, as modeling-free inversion-based iterative
control (IIC). A learning law is derived for a nonlinear system,
where the internal system identification is formulated as an
estimation problem of a Jacobian matrix that represents the
system. In order to find a suitable Jacobian estimation method
in the IIC, this paper compares Broyden´s method and the
linear method, as well as the secant method. To decease the
algorithms, the IIC is operated only at the harmonic frequencies
of the motion trajectory. In the implementation of the modelingfree
IIC, the control input update is explicitly separated from
the Jacobian estimation, so that the IIC can still decrease the
motion error even when the Jacobian estimation is interrupted
for stability. The experimental results demonstrate that the
secant method is the best of the three for raster scanning due
to its fast learning and high tracking performance.

https://publik.tuwien.ac.at/files/publik_260451.pdf