This article proposes a gated recurrent unit (GRU) neural network prediction and compensation (NNC) strategy for precision multiaxis motion control systems with contouring performance orientation. First, some characteristic contouring tasks are carried out on a multiaxis linear-motor-driven motion system, and the true contouring error values obtained by the Newton numerical calculation method are used as the training data of a developed artificial GRU neural network. Essentially, the proposed GRU neural network structure can be viewed as a data-based black-box error model, which can capture the dynamic characteristics of contouring motion rather accurately. The well-trained GRU network can predict the contouring error precisely even under the tasks those have not been conducted during the training session. Moreover, the predicted contouring error is compensated into the reference contour as feedforward compensation to improve the final contouring performance. Comparison between the predicted contouring error and the actual contouring error practically proves the effective prediction ability of the proposed GRU neural network. Furthermore, comparative experiments among proportional-integral-differential, iterative learning control (ILC), and the proposed NNC controller are conducted. The results consistently validate that NNC can basically achieve excellent contouring motion performance as ILC, significantly without need of motion repetition and iteration. Due to the implementation convenience and excellent prediction/compensation ability, the proposed NNC would have good potential in industrial mechatronic applications.

To simultaneously achieve accurate tracking error prediction, rigorous motion accuracy, and certain robustness to parameter variations and unknown disturbances, this article proposes a data-based learning adaptive robust control (LARC) strategy based on gated recurrent unit (GRU) neural network. Firstly, parameter adaptive control and robust control are utilized to guarantee the robustness against parametric uncertainties and unknown disturbances. A GRU neural network is then constructed and capable of precisely predicting the tracking error after training with data collected from a linear-motor-driven stage. Essentially, the GRU network can be viewed as a data-based model, which captures the tracking error dynamic characteristics and provides a prediction even before implementing the real trajectory. Consequently, a reference modification and a feedforward compensation part can be formed, which is the significant part of the whole LARC control structure. Comparative experimental investigation not only validates the effectiveness of the tracking error prediction ability, but also demonstrates the practically satisfactory transient/steady-state tracking performance of the proposed control strategy.

In this paper, a global task coordinate frame (GTCF)-based learning adaptive robust contouring controller is proposed for an industrial X-Y linear-motor-driven stage to achieve not only good parametric adaptation ability and disturbance robustness, but also excellent contouring accuracy even under high-speed large-curvature contouring tasks. Specifically, the contouring controller employs GTCF to guarantee the multiaxes motion coordination. After transforming the system dynamics of the X-Y linear-motor-driven stage into the GTCF, a learning adaptive robust control (LARC) scheme is developed to deal with the strongly coupled dynamics under parametric uncertainty and uncertain disturbances. During the LARC, adaptive model compensation term, robust feedback term, and iterative learning term are organically integrated in a serial structure. The controller design process with the stability analysis is presented, while the essence of the practical achievable performance is also introduced for the nature of the GTCF-LARC. Comparative experiments are carried out on an industrial linear-motor-driven stage with different cases. The results consistently verify that the proposed GTCF-LARC contouring controller can simultaneously meet the industrial requirements of excellent transient/steady-state contouring accuracy, parametric adaptation ability, external disturbance robustness, and large-curvature high-speed contouring tasks. The proposed GTCF-LARC scheme actually provides a practical high-performance-oriented contouring control framework, and could be extended to other multiaxes applications.

In this article, to guarantee the good tracking performance of the precision motion system for various tracking tasks, an online iterative learning compensation method is proposed for closed-loop motion control systems. The prediction model is based on the closed-loop model of the linear second-order system with a proportional-integral-derivative controller, and an estimation term is added to deal with the influence of slow-varying uncertain disturbances. On the basis of the accurate state prediction, the dynamical feedforward compensation can be obtained, which suppresses the tracking error caused by the dynamical lag. Furthermore, in order to simultaneously compensate the errors caused by nonlinear factors such as uncertain disturbances and to guarantee the smoothness of the compensated trajectory, the optimal compensation gain is determined through online iterative calculation. The online iterative approach is similar to iterative learning control, but does not require several offline iterations of a repeating trajectory. Comparative experiments are carried out on an industrial motion stage. Various experimental results consistently demonstrate that the proposed compensation scheme can achieve the tracking accuracy comparable to iterative learning, while maintaining the robustness to trajectory changes and uncertain disturbances without reoffline iteration.

This paper proposes a Newton extremum seeking algorithm based iterative learning coordinated control (Newton-ILC) strategy for contouring motion accuracy of precision multiaxial systems. Specifically, as the contouring error estimation is critically important for coordinated contouring motion control, a cost function is constructed based on the reference contour, as well as the current position, and the minimal value of the function is searched to determine the contouring error point through an offline Newton algorithm. Consequently, high precision estimation of the contouring error can be achieved, even under extreme contouring tasks with high speed, large curvature, and sharp corners. The calculated contouring error is then projected to each axis, and the axial contouring errors are controlled by iterative learning method, while the learning results will be used to adjust the axial position reference commands for contouring accuracy improvement. Comparative experiments are conducted on a biaxial linear motor stage to validate the practical effectiveness of the proposed Newton-ILC strategy. The experimental results illustrate that the proposed Newton-ILC achieves not only nearly perfect contouring error estimation but obvious improvement of contouring accuracy as well after a few iterations. Particularly, in some extreme cases such as large initial tracking error, high speed, large curvature, and sharp corners, the proposed Newton-ILC strategy can achieve rather excellent contouring performance when compared with individual axis control, conditional cross-coupled control, and cross-coupled iterative learning coordinated control (CCILC) methods.

In order to simultaneously provide excellent tracking performance as well as good generalization for precision motion control of magnetically levitated (maglev) planar motors, this article proposes a feedforward compensation strategy with precise reference modification prediction using gated recurrent units (GRU). First, a GRU network is constructed, which is capable of precisely predicting the reference modification after training with data collected from a maglev planar motor. Essentially, the GRU network can be viewed as a data-based model which captures the dynamic characteristics of appropriate reference modification and gives a prediction even before implementing the real trajectory. Consequently, an excellent feedforward compensation part can be formed, which is important in the whole control structure. Comparative experimental investigation validates the effectiveness of the GRU-based modification prediction ability and demonstrates the excellent tracking performances of the proposed control strategy. The proposed strategy not only performs as well as iterative learning control, but also does not need any time-consuming iterations, which is valuable for industrial applications.