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.

When the trajectory with high speed and high acceleration contains frequency contents matching with the structure mode, the inertial vibration of the structure is easily excited, reducing machining accuracy and surface finish. Input shaping can avoid vibration, but it introduces time-delay that causes multiaxis trajectory distortion and affects the accuracy of contour error estimation. This article presents time parameter mapping and contour error precompensation for multiaxis input shaping to suppress vibration. The mapping of time parameter domain of trajectories is established by deducing the relation between the local curvature extremums of the trajectories before and after shaping, which provides reference points for contour error estimation. The actual trajectory is predicted by the closed-loop servo dynamics model and reference trajectory, and then the Newton iterative algorithm based on time parameter mapping is used to seek the contour error point. Finally, the calculated contour error is low-pass filtered and projected to each axis, and then the shaped trajectory is precompensated to simultaneously reduce the contour error and avoid structural vibration. Comparative experiments are conducted to validate the effectiveness of the proposed method. Experimental results illustrate that the proposed method not only suppresses structural vibration, but also significantly improves the estimation accuracy and contouring performance by time parameter mapping.

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.

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.

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.

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.