The application of linear motor-driven stages as the feed drivers of CNC micro milling machine tools is growing. In addition to employ high speed and high precision equipment such as linear motor-driven stages, the precision of the machined contours is highly dependent on the capabilities of the servo controllers. In this paper, the design of a precise controller for a two-axis LMDS has been investigated for micro-milling applications. In such feed drives, disturbances such as friction, force ripples, and machining forces have adverse effects on the workpiece positioning precision due to the direct drive concept behind them. Therefore, in order to have an acceptable transient response and disturbance rejection properties, a two-degree-of-freedom proportional-integral-derivative controller was employed for each axis. To design this controller, the zero-placement method was used. To compensate disturbances and machining contour errors, the utilization of Kalman filter observers, neural networks, cross-coupled controllers, and different integration of them were studied. The controllers were experimentally examined for circular motions. An integrated controller consisted of a Kalman filter disturbance observer, a cross-coupled controller, and a well-designed two-degree-of-freedom proportional-integral-derivative controller resulted in a high contouring and tracking precision. The controller could also reduce the spikes caused by the friction at the motion reversal points such as the quadrants in circle trajectories.

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This paper introduces a new rigid finite element method (RFEM) formulation for dynamic analysis of plates. In RFEM, a flexible body is divided into several rigid elements which are interconnected by spring and damping elements. Mainly, RFEM has been used to model systems with beam-like slender components, such as ropes and cables, and few RFEM formulations were developed to model plates and shells. In this study however, by means of the Timoshenko beam theory and cuboid rigid elements, a novel RFEM formulation is developed to model flexible flat plates with generic geometries of the surface, considering large deformation. For this purpose, an RFEM formulation is presented for straight beams with rectangular cross-section by means of the Timoshenko beam theory. Next, this formulation is expanded to model flexible rectangular plates with uniform thickness and then, it is elaborated on how to model non-rectangular plates with uniform thickness using only cuboid elements and consequently, the development of the proposed RFEM formulation is completed. After investigating various case studies, the competence of the proposed formulation is evaluated thoroughly. The results of RFEM came on a proper agreement with the FEM results in a way that the maximum difference between these results in dynamic analysis was about 3%.