Application of the adaptive fuzzy wavelet neural network for two‐axis trajectory control*.

The accuracy of contour tracking is an important issue to be addressed for the X‐Y stage in a machining tool. Applying a better control scheme can help to increase the tracking accuracy with the effects of systems' uncertainties, nonlinearities and disturbances. In this paper, to prevent these negative effects and achieve high accuracy tracking control of the two‐axis motion stage, the adaptive fuzzy wavelet neural network (AFWNN) PI sliding mode controller is proposed. The adaptive algorithm is combined with the basis function of the wavelet neural network and fuzzy system to approximate the plant model functions. Then, the controller with PI sliding mode structure could be built based on the estimated system function. In this method, the time domain positioning property of wavelet and the reasoning of the fuzzy system could provide the well‐estimated plant model. Moreover, the adaptive algorithm and sliding mode control scheme help to reduce the effects of parameter variation and uncertainties. The stability is analyzed via Lyapunov stability theorem to prove the asymptotic stability of the system. In the simulation and experimental results, the contours are planned through the nonuniform rational B‐spline (NURBS), which is considered a high accuracy interpolator. The tested curves consist of circle, bow, heart, star and trident. The average and standard deviations of the tracking errors are compared to other methods to illustrate the performance of the proposed method. The results demonstrate that the method can reduce errors more effectively and have better localization for trajectory tracking. [ABSTRACT FROM AUTHOR]