Contour control is an important task for many motion control applications. This paper reviews the state-of-the-art control methods in academic research for contour tracking, including individual axis tracking control, cross coupled control and its variants, and other contour control methods, such as neural networks and velocity field control. Different methods for contour error estimation are also reviewed. Areas for future multiaxis contour control research are discussed.

Multiaxis Contour Control—the State of the Art

A contouring controller for biaxial systems that integrates the effects of feedback, feedforward, and cross-coupled control is proposed in this study. Conventional approaches to contouring control suffer from the complicated contour-error model and from lack of a systematic way for controller design. The integrated controller is based on polar coordinates under which a relatively simple contour-error model can be obtained. Taking the simple contour error as a state variable, the contouring-control problem is transformed into a stabilization problem. The feedback-linearization technique incorporated with linear feedback or robust control (such as sliding-mode control) can then yield the integrated controller. The proposed method is verified both numerically and experimentally and is compared with the conventional approach. It is found that the proposed controller is better for high speed and/or noncircular contouring. In addition, it can be applied to either linear plants or nonlinear plants (like linear motors).

Contouring control of biaxial systems based on polar coordinates

This study is concerned with the contouring control for multiaxis (n-axis) motion system. The equivalent errors, consisting of n - 1 equivalent contour errors and 1 tangential error, are proposed to simplify the design of contouring controller. Instead of the actual contour error, which is, in general, a complicated function of axial positions, the equivalent errors are taken as the new control objective. The contouring control problem becomes the stabilization of the equivalent errors. To this aim, the method of integral sliding mode control is employed. The proposed method can be applied to both linear and nonlinear plants following arbitrary smooth paths. Numerical and experimental results on an XY table driven by linear motors clearly verify the theoretical analysis. An experimental comparison of the proposed method with conventional methods is also provided for an XY table driven by conventional motors. The results show that the proposed method is especially useful for high-speed contouring applications.

Contouring Control of Smooth Paths for Multiaxis Motion Systems Based on Equivalent Errors

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.

Newton-ILC Contouring Error Estimation and Coordinated Motion Control for Precision Multiaxis Systems With Comparative Experiments

Contour control is an important issue in motion system development. In this paper, a contour-control methodology combining predictive control and adaptive feed rate is proposed. To reduce the computational time required for online optimization, a simple unconstrained model predictive controller is first designed to perform biaxial contour-position control. The performance index introduced in this paper allows the designer to manipulate the importance between contour error, axial tracking error, and control usage. The controller is then implemented to track diamond and free-form contours. The results demonstrate that the controller is capable of not only tracking both contours with high precision (contour and axial) for steady motions, but also improving contour precision during transient periods. To further reduce the contour error during transient periods, an adaptive feed-rate scheme is proposed, which utilizes the predicted contour error to adjust the feed rate online. This adaptive feed-rate scheme is experimentally validated using diamond and limacon contours. The results demonstrate that in comparison with constant feed-rate schemes, the proposed adaptive feed-rate scheme is capable of significantly reducing the transient contour error at high feed rates, while maintaining comparable tracking performance at low feed rates.

Predictive Contour Control With Adaptive Feed Rate

In biaxial contour tracking applications, the main concerns are the tangential and the contour errors. This paper presents a tangential-contouring controller to achieve effect and decoupled control of these concerns. The proposed controller is based on a coordinate transformation between the X-Y frame and a tangential-contouring (T-C) frame that is defined along the contour. Experimental evaluation for the proposed controller is conducted on a biaxial positioning table.

Tangential-Contouring Controller for Biaxial Motion Control

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Tangential-Contouring Controller for Biaxial Motion Control