Iterative learning control (ILC) achieves high control precision across various motion systems during repetitive tracking tasks by successively updating the compensation. In identical control circumstances, tracking errors primarily comprise repetitive components to be eliminated, induced by the input signals and regular system disturbances. In order to mitigate repetitive errors efficiently, conventional ILC methods treat the high-frequency components of tracking errors as nonrepetitive noise and disturbances, employing the low-pass filter to exclude these components. However, this specific frequency criterion is not entirely accurate, as there can be interference in the low-frequency range and effective components in the high-frequency range. Therefore, an energy-selected ILC is proposed in this article to identify these components, thereby enhancing the filtering validity. The proposed method proposes a novel energy criterion to construct the robust filter, improving the capability to distinguish repetitive components. Based on this advanced robust filter, the trajectory modification is designed as the learning filter to accelerate the convergence rate. The stability and convergence of this method are thoroughly proven and analyzed. Various comparative experiments have been conducted to illustrate the effectiveness of this novel energy-selected ILC approach. Generally, the proposed method has the following superiorities: it achieves high control precision across various motion scenarios; it broadens wide bandwidth applicable in high-frequency and nonsmooth circumstances; and it has an accurate error analysis suitable for practical applications. Meanwhile, it improves the control performance of classic ILC while maintaining its ease of implementation.

In the realm of ultraprecision motion control, achieving high tracking accuracy, great trajectory generalization, and robust disturbance rejection simultaneously remains a challenge. This article proposes an intelligent gated recurrent unit real-time iterative compensation (GRU-RIC) position-loop feedforward compensation control method to tackle this issue. Specifically, a gated recurrent unit (GRU) neural network is first trained to accurately predict tracking errors for given reference trajectories in advance. The predicted error serves as an offline feedforward compensation signal to enhance tracking accuracy. To mitigate residual tracking errors arising from incomplete offline compensation and unexpected disturbances, a real-time iterative compensation (RIC) scheme that generates optimal online feedforward signals through real-time system prediction is proposed. Both offline and online compensation signals are synergistically applied to modify the reference trajectory in a position-loop feedforward manner. Experimental results on a nano-precision air-bearing motion stage confirm that the GRU-RIC method achieves 10-nm tracking accuracy, which is the same as iterative learning control (ILC), while outperforming ILC in trajectory generalization and disturbance rejection.

This article presents a novel real-time iterative compensation (RIC) method using plant-injection feedforward architecture for motion control of ultraprecision wafer stages, addressing the severe challenge of achieving extreme tracking accuracy along with strong task flexibility and disturbance rejection ability. The RIC method establishes an online prediction model to accurately predict upcoming tracking errors during real-time motion. The prediction result enables the online generation of optimal plant-injection feedforward signal at each sampling control instant via iterative calculation, which enhances tracking accuracy and dynamical regulation capability. Various trajectory tracking tasks have been implemented on an ultraprecision wafer stage. Experimental results demonstrate that RIC matches the high tracking accuracy of well-acknowledged iterative learning control while offering superior task flexibility and disturbance rejection ability.

Time-optimal trajectory planning aims to minimize the traversal time of arbitrary geometric paths. The demand for real-time planning widely exists in robotics, numerical control manufacturing, and autonomous vehicle applications. Existing trajectory planning methods either compromise on time optimality to improve computational efficiency or suffer from at least linear time complexity, preventing the planning of long trajectories in real time. Motivated by these challenges, this article proposes a novel set invariant trajectory planning (SITP) method to address the problem of real-time time-optimal planning for continuous multiaxis trajectories under complete second-order kinodynamic constraints. First, a backup control strategy is synthesized to construct an implicit control invariant set (CIS). This set is designed so that a feasible control input always exists to keep the system within the defined kinodynamic bounds. Then, utilizing the principles of bang–bang control theory, the optimal control is sought within the CIS. A local greedy linear programming method is proposed to calculate the time-optimal trajectory at each control cycle. The proposed method is computationally efficient for even 1-kHz real-time applications and the planned results maintain strict global time optimality, which makes it promising in real-time planning scenarios of various automatic applications.

Hybrid additive-subtractive manufacturing (HASM) has achieved universal application in aerospace, medicine, military industry, and other fields. The additive manufacturing (AM) process has a significant influence on manufacturing quality and efficiency in HASM. However, few process planning methods exist utilizing the interplay between different processes in HASM. For the first time to the best of our knowledge, this paper proposes a slice extension (SE) method for HASM, the key idea of which is to print an extended slice in the AM process and guarantee the final geometric accuracy in the subtractive manufacturing (SM) process. Firstly, an optimization problem minimizing the isoperimetric quotient, the area, and the perimeter of the extended slice, is designed and convexified. Then, a unilateral rolling circle (URC) method is proposed to guarantee that the extended slice covers the original slice. Finally, an approach to dealing with multiply connected slices is proposed to eliminate underfill near holes. Simulation experiments indicate that the proposed SE method achieved an 81.5% lower underfill rate than the conventional method, i.e., the widely-used contour-parallel (CP) method in the industry, with limited extra materials on average. The toolpath smoothness is also improved. The performance of the proposed SE method verifies its significant application potential in HASM, computer numerical control milling, and other fields.

The aim of this article is to propose a novel rational feedforward tuning method, by directly mapping the feedforward signal learned by dual-loop iterative learning control (DILC) onto the corresponding reference, that achieves high performance for varying trajectory tracking tasks. The DILC algorithm is first developed by paralleling the standard iterative learning control (ILC) with an additional iterative loop. Different from the standard ILC, DILC can learn an ideal feedforward signal eliminating the reference-induced error even though a robustness filter presents for the robust convergence against model uncertainties. Then, based on the reference and the feedforward signal learned by DILC, an instrumental variable-based algorithm is developed for the parameter tuning of the rational feedforward controller, which leads to unbiased estimates and optimal accuracy in terms of variance. The proposed method combines the performance of DILC with the flexibility of rational feedforward controllers. Comparative simulation and application to an ultraprecision wafer stage illustrate the enhanced performance of the proposed approach compared to the preexisting results.

Back electromotive force (EMF)-based sensorless control strategies for permanent-magnet linear synchronous motor (PMLSM) have the potential to simplify the mechatronic system, reduce the cost and prolong the service life. However, the poor performance in the low-to-zero speed region limits their application range. In this article, a novel back EMF-based mover position estimator is proposed to achieve consistent good accuracy in the whole speed range including high speed, medium speed, low speeds, temporary standstill, and speed reversals. The three-phase flux linkages are obtained by directly calculating the integration of back EMF. To overcome the curve drift caused by the integrator, this article proposes a jumping correction algorithm and a uniform correction algorithm. The mover position is calculated from the corrected flux linkages. This article also realizes a closed-loop sensorless trajectory tracking control system using the proposed position estimator. Experimental results on a PMLSM demonstrate that the proposed position estimator can guarantee the stability and accuracy in the whole speed range. Compared with the existing back EMF-based methods working only well in high-speed region and usually with$mm$-level accuracy, the proposed method achieves an accuracy of sub-200$\mu$m regardless of the reference trajectory, and has exciting prospect in industrial applications.

For precision motion systems widely applied in industrial manufacturing equipments, it is critical to achieve both high trajectory tracking accuracy and superior disturbance rejection ability. In this article, a novel nonlinearity compensation and high-frequency flexibility suppression based real-time iterative compensation (RIC) method is proposed to achieve excellent tracking performance in practice. The unexpected nonlinearity and high-frequency flexible mode of the plant, which limits the achievable control performance, is first compensated and suppressed. Subsequently, a RIC method based on accurate linear prediction model is proposed to further reduce the tracking error by adding a compensation term to the initial reference trajectory. The trajectory compensation idea of RIC is comparative to remarkable iterative learning control (ILC), but the proposed RIC can online generate and adjust the compensation term during real-time motion without abundant offline iteration trials in ILC. This mechanism significantly enhances the robustness to trajectory variations and external disturbances. Comparative experiments carried out on a ball-screw-driven precision motion stage with full-closed loop position feedback validate the effectiveness and superiority of the proposed method for various trajectory tracking tasks. The proposed method outperforms ILC on tracking performance, and possesses the robustness to various disturbances and reference variations, which leads to industrial application significance.

GaoFen-3 (GF-3) is a C-band multipolarization synthetic aperture radar (SAR) satellite with 12 imaging modes. However, its initial positioning accuracy remains unsatisfactory, thereby hindering its use for large-area surveying and mapping. This study proposes a block orthorectification method without ground control points (GCPs) using the GF-3 Fine strip II (FSII) mode. To address the challenges with the accuracy and efficiency of this method, an integrated block orthorectification method was developed to conduct integrated processing of large-scale GF-3 satellite images without GCPs. Geometric calibration was used to improve the absolute positioning accuracy of each SAR image. Then, several tie points (TPs) were extracted using the SAR scale-invariant feature transform (SIFT) operator. A parallel matching strategy was used in the block images registration. The block adjustment model was constructed to solve the orientation parameter of all SAR images. The experimental results of 1,468 GF-3 images of China’s entire land area show a TPs root-mean-square error of 0.724 pixel and 8.014 m for the independent checkpoint, suggesting that the proposed method can effectively improve the geometric accuracy of GF-3 satellite images and demonstrate the feasibility of large-scale SAR mapping without GCPs.

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.

Decoupling control is still an important research topic for precision multiple-input-multiple-output (MIMO) motion systems involved in computer numerically controlled (CNC) machine tools, wafer scanners, etc. In this paper, to minimize internal coupling and improve servo performance, a data-based iterative dynamic decoupling control (IDDC) approach is synthesized. Specifically, a MIMO dynamic decoupling controller structured with finite impulse response filter is used as an add-on to a static decoupling part. Then, a data-based parameter optimization algorithm is developed such that the optimal parameters can be iteratively solved based entirely on the input/output data by minimizing the coupling-induced error. Unlike pre-existing IDDC approaches, the proposed approach can achieve an unbiased estimate of the optimal parameters combined with a small estimate variance that is illustrated through numerical simulation. Finally, application to an ultraprecision wafer stage confirms that the proposed approach significantly decreases the coupling-induced error and achieves enhanced performance compared to pre-existing approaches.

Contouring motion control plays an important role in modern precision multiaxis motion systems. In order to enhance the coordination between each axis and promote contouring performance, many research works have been conducted that mainly focus on contouring error online estimation and control. Essentially, most of existing control strategies based on emerged contouring error belong to feedback control, which cannot achieve perfect performance due to inevitable delay or lag. To fundamentally tackle the above problem, a novel position-loop feedforward contouring control method is proposed in this paper. Specifically, according to the linear model of each axis and the kinematics characteristics of reference contour, a dynamical model of contouring error in multiaxis systems is firstly developed, which can explain the essential causes of contouring error quantificationally. Then, based on the proposed contouring error model, a position loop feedforward control strategy can be designed for contouring following tasks. The effectiveness of the proposed method is tested on a three-axis computerized numerical control systems. Various experimental results consistently demonstrate that the contouring error model can accurately predict actual contouring error to some degree. Compared with the conventional model-based feedforward approach, the proposed strategy can not only point out the essential causes of contouring error directly, but also achieve better contouring performance.

Sometimes the result of single tracker can be unreliable under some situation like illumination variation, occlusion, object size change, etc. Combining multiple estimates is a usually strategy to improve the performance of visual tracking, the ensemble approach can combine the advantages of difference models and overcome this limitation. In order to better fuse the results, we propose an adaptively fusion method that can select the weight of each track result automatically. Moreover, we propose an adaptively update strategy to avoid the “drift” during tracking. The assemble method and update strategy are selected by analyzing the situation of tracking response map. We expand Staple using our methods and evaluate the performance on famous object tracking benchmark. Experimental results show that our proposed method outperforms state-of-the-art tracking methods.

In this paper, a neural network learning adaptive robust controller (NNLARC) is synthesized for an industrial linear motor stage to achieve good tracking performance and excellent disturbance rejection ability. The NNLARC scheme contains parametric adaption part, robust feedback part, and radial basis function (RBF) neural network (NN) part in a parallel structure. The adaptive part and the robust part are designed based on the system dynamics to meet the challenge of parametric variations and uncertain random disturbances. It must be noted that in actual industrial machining situations, precision motion equipment is always disturbed by unknown factors, which usually cannot be described by mathematical models but affect the tracking accuracy significantly. Therefore, the RBF NN part is employed to further approximate and compensate the complicated disturbances with high reconstructing accuracy and fast training rate. The stability of the proposed NNLARC strategy is analyzed and proved through the Lyapunov theorem. Comparative experiments under various external disturbances such as completely unknown disturbance added by polyfoam are conducted on an industrial linear motor stage. The experimental results consistently validate that the proposed NNLARC control strategy can excellently meet the challenge of complicated disturbance in practical applications. The proposed scheme also provides a guidance for control strategy synthesis with both good tracking performance and disturbance rejection.

Wafer stage is an important mechatronic unit of industrial lithography tool for manufacturing integrated circuits. To overcome the inherent limitations of fix-gain feedback control and improve the servo performance, a performance-oriented variable-gain control strategy with accelerated iterative parameter tuning is proposed for an ultra-precision wafer stage. The variable-gain controller comprises a fix-gain proportional-integral-derivative (PID) controller and add-on variable-gain elements, which are the focus of this paper. Specifically, the add-on variable-gain elements are significantly designed based on the main tracking error sources and error frequency of different reference trajectory phases. A weighted two-norm regarding the performance indexes of wafer stages, i.e., moving average (MA) and moving standard deviation (MSD) of the tracking error, is synthesized as the objective function, and the data-driven Levenberg–Marquardt-based iterative parameter tuning scheme is employed to find the optimal parameter values of the proposed variable-gain controller. Furthermore, to improve the convergence rate, a multiparameter accelerated iterative method is developed based on Aitken’s method. Finally, the proposed variable-gain control strategy is implemented on an ultra-precision wafer stage developed in our laboratory. Comparative experimental results demonstrate that the strategy performs best and achieves excellent improvement on both MA and MSD. During the scanning phase, MA and MSD are less than 1.02 and 2.35 nm, respectively. The proposed variable-gain control strategy is also suitable for other industrial applications.

Recently, the minimum error entropy (MEE) criterion has been used as an information theoretic alternative to traditional mean-square error criterion in supervised learning systems. MEE yields nonquadratic, nonconvex performance surface even for adaptive linear neuron (ADALINE) training, which complicates the theoretical analysis of the method. In this paper, we develop a unified approach for mean-square convergence analysis for ADALINE training under MEE criterion. The weight update equation is formulated in the form of block-data. Based on a block version of energy conservation relation, and under several assumptions, we carry out the mean-square convergence analysis of this class of adaptation algorithm, including mean-square stability, mean-square evolution (transient behavior) and the mean-square steady-state performance. Simulation experimental results agree with the theoretical predictions very well.