A Path Control with Vector Decomposition by Means of Expansionary Coordinate Transformations

Abstract

We propose a new path control method with vector decomposition by means of expansionary coordinate transformations in this paper. In the present study, a motion equation of multiaxial systems in an orthogonal coordinate system is transformed into a rotational coordinate system whose axes are expanded. Then, an arbitrary curve path can be transformed into the circle or straight line path using the transformations. The transformed motion equation can be decoupled and decomposed into a gain component and a phase component. Both the gain component and the phase component control system are constructed independently. In the transformed area, the desired value of the gain component becomes constant and the gain component error is equal to the path error which can converge to zero by using 1-type controller. The effect of disturbances will be absorbed by the phase component control system and the path error is little disturbed. In the proposed method, essential path control can be realized using the unity control coefficient over a wide range, from the desired curved line path to the straight line path. The proposed control method is applied to multi-axis linear motor tables, and the effectiveness of this method is confirmed experimentally.