Comparison of modeling-free learning control algorithms for galvanometer scanner's periodic motion

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 modeling-free 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.