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 order to achieve both accurate contouring error estimation and excellent contouring control performance for multi-axis motion systems, this paper proposes an online iterative pre-compensation control method based on third-order contouring error prediction model. Specifically, the closedloop dynamical model of each axis is firstly used to predicate tracking errors at future sampling instants. And then the related contouring error of multi-axis system at future time can be expressed by the predicted tracking error and the theoretical third-order model of the reference contour. To reduce the influence of modeling error and uncertain disturbances on the prediction performance of contouring error, the numerical calculation method is utilized to obtain absolutely accurate contouring error, through which the deviation between the proposed contouring error model and the accurate one can be corrected accordingly. Based on the accurate contouring error prediction model, the optimal contouring error compensation can be generated through online iterative calculation. To achieve excellent contouring performance, the compensation is added to the original reference contour as a kind of trajectory precompensation. Comparative experiments are carried out on an industrial three-axis machine tool. A series of contour tracking experiments consistently demonstrate that the proposed method can predicate the contouring error accurately. Additionally, the contouring motion performance can also be significantly improved in the case of a variety of different trajectories.

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.