Study Of Contour Control For Direct Drive X-Y Table Based On Equivalent Errors

To weaken the influences of nonlinear system dynamic, uncertainties, and complex contour error model of curve trajectory for direct drive numerical control X-Y table servo system driven by Permanent Magnet Linear Synchronous Motors (PMLSM), the equivalent errors method applicable for multi-axis nonlinear motion system is adopted to establish equivalent errors model, and a compound control scheme based on IP feedback and feed forward control combined with second order sliding mode control is presented in this thesis, enhancing the contour error precision of X-Y table linear servo system.Firstly, the development, application, construction and work principles of direct drive X-Y table were introduced in this paper. Mathematical models of single axis permanent magnet synchronous linear motor (PMLSM) and X-Y table were established. According to the characters of X-Y table, the factors that affect the contour precision were analyzed. Direct drive technology eliminates the middle transmission parts and has the merits of large thrust, low friction, high dynamic stiffness and high positioning precision. However, X-Y table is sensitive to the uncertainties and nonlinear factors that its servo performance decreased, so it is necessary to design servo controllers to improve the robustness and contour precision.Secondly, the traditional Taylor approximate contour error model was established. The single axis coordinate contour controller and cross-coupled contour controller were designed to improve the contour precision and dynamic performance of X-Y table. Single axis coordinate contour control emphasizes on reducing the contour error through reducing single axis tracking errors. Cross-coupled contour control combines the tracking errors first and generates corresponding compensate gains to each axis.Thirdly, the equivalent errors method applicable for multi-axis nonlinear motion system was adopted. Based on the established nonlinear equivalent error model including the equivalent contour error and tangential error that easily calculated and suitable for general curves of XY stable, the contour control problem was converted to the stabilization of error dynamic system. Through feedback linearization and pole assignment control, the equivalent errors approached zero.Last, in view that the contour control based on feedback linearization and pole assignment can't resolve the effects of uncertainties and in order to improve the contour accuracy and robustness of linear motor XY table, the second order sliding mode contour controller is designed. Then the sliding mode surface and its derivative approach zero in finite time. The effects of chattering and uncertainties are reduced and the equivalent errors approach zero.Yokogawa LM110 permanent magnet linear synchronous motor X-Y table is considered as the controlled object, its mathematical model is established, and it is necessary to simulate and analyze above control strategies using MATLAB software. Simulation results show that compared with traditional single axis coordinate contour control,cross-coupled contour control and pole assignment control based on feedback linearization, the proposed second order sliding mode control method based on equivalent errors method can enhance the robustness and contour precision of X-Y table linear servo system.