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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]

Real systems with nonlinearity and valuable information always have unpredictable meaning and chaos properties in nature. It is often difficult to obtain the system model based on set of stimulus and response samples due to its complexity. This paper proposes the type-2 fuzzy neural network (T2FNN) and its learning method using grey wolf optimizer (GWO) for system identification. The structure of T2FNN is a combination between a type-2 fuzzy logic system with human-like IF-THEN rule thinking properties and neural networks (NN) with learning and optimization capability. The GWO is a meta-heuristic algorithm inspired from the social hunting behavior of grey wolves as search agents. This method is investigated by strategy, which maintains a proper balance between exploration and exploitation processes and gives more importance to the fittest to find the new position of search agent during the iterations. The GWO algorithm is considered for learning method due to its advantages, including high accuracy, very effective and more competitive. To evaluate the proposed system, the T2FNN with GWO learning method is employed by several nonlinear problems, including single-input single-output systems and multi-input multi-output (MIMO) systems. They are Mackey-Glass chaotic data series, nonlinear plant, nonlinear dynamical time-varying plant, and two MIMO systems. The merits of the proposed learning algorithm can be defined through experiments of the model and compared with existing learning PSO and GA algorithms and previous studies in literature. Based on the experimental results and performance comparisons, the proposed GWO algorithm indeed obtains the enhanced performance and capability in terms of the root mean squared error for nonlinear system identification applications. [ABSTRACT FROM AUTHOR]