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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]

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]

Nonlinear time series analysis and forecasting are an essential part in a diverse range of physical and natural applications. This paper presents a time-division cerebellar model articulation controller (TDCMAC) network using a modified biogeography-based optimization (modified BBO) learning algorithm for nonlinear time series and measurement data prediction. The TDCMAC method is a time windowing strategy constructed using the CMAC network. BBO algorithm is designed related to the geographical distribution of species over time and space. This study presents two modified migration functions of the essential BBO, i.e. quadratic migration BBO (QBBO) and sinusoidal migration BBO (SBBO) methods, to improve convergence rate and quality of solution. Five nonlinear time series, including Mackey-glass, Lorenz, Rossler, Limber Pine, and Ponderosa Pine data series, are employed to investigate the proposed predictor. The TDCMAC networks using QBBO and SBBO learning algorithms are compared with the gradient descent (GD) method and other existing heuristic learning methods, including particle swarm optimization (PSO), genetic algorithm (GA), and conventional BBO methods, to verify the estimation performance of the proposed method. The performances are evaluated through an extensive simulation by computing the root mean square error (RMSE), mean absolute percentage error (MAPE), and average relative variance (ARV) metrics. Experimental results demonstrate that the proposed predictor indeed achieve more accurate performances and faster learning speed for time series prediction applications. [ABSTRACT FROM AUTHOR]

In this study, the authors present a control method for the permanent magnet synchronous motor (PMSM) driven X–Y motion system for application in industrial and manufacturing apparatus. Backlash and friction effects in ball‐screw actuated systems are common obstacles to achieve high‐accuracy control. The authors investigate the indirect fuzzy controller to demonstrate the feasibility of reference trajectory tracking and derive an adaptive law in the error state space to deal with parameter uncertainties and external disturbances. The authors adjust the fuzzy parameters online, based on the Lyapunov stability theorem, such that the asymptotic stability of the whole system and error convergence can be guaranteed. In the authors' experiments, this indirect fuzzy control approach compensated for the non‐linear friction and disturbance variation of the biaxial linear stage following the application of four contour shapes, i.e. square, triangular, star, and circular reference contours. Both the authors' simulation and experimental results demonstrate substantial improvement in contour tracking performance in terms of average tracking error and tracking error standard deviation, as well as robustness against platform uncertainties. [ABSTRACT FROM AUTHOR]