Research On Three-dimensional Contouring Error Estimation And Contouring Control

Tracking error of a multi-axis servo system is defined as the vector from the current end-effector's position to the current desired position.Traditionally,reducing tracking error is the main objective in motion control.However,the contouring error,which is the distance from the current end-effector's position to the desired contour,is crucial to the surface quality of the final workpieces.Compared with tracking error control,the direct control of contouring error can effectively improve machining quality.However,the calculation of contouring error for free-form contour is complicated and time consuming.In order to control contouring error in real-time,the improvement of contouring error estimation accuracy and real-time capability are necessary.However,the existing researches mainly focus on two-dimension contouring control.Controller designing and control parameters tuning process are complicated for three-dimension contouring control.In this thesis,three-dimension contouring control is discussed based on three-dimension contouring error estimation method,reduced-dimension contouring control and cross-coupled control.The effectiveness of the proposed methods is tested on a three-axis machine tool and a parallel robot.Most existing contouring error estimation methods are difficult to be used in three-dimension contouring control since the insufficient estimation accuracy.In this thesis,a high-accuracy contouring error estimation method is proposed for three-dimension contouring error estimation.In Frenet frame,a novel canonical approximation is proposed based on the third-order Taylor expansion on the current desired position.Then,the mathematical expressions of traditional tangential and circular approximation are given for comparison.From the mathematical expressions and the concept of the contact order,the tangential approximation,the circular approximation,and the canonical approximation are discussed.The canonical approximation is the simplest form which has the same function value,curvature,and torsion on expansion position.The canonical approximation is the method that considers both estimation accuracy and computation efficiency for three-dimension contour error estimation.Since the controller designing and control parameters tuning are complicated in traditional contouring control,a task orthogonal coordinate frame and a task polar coordinate frame are proposed.Based on the coordinate transformation from the world Cartesian coordinate frame to the proposed coordinate frames,the contouring performance and advancing performance can be individually controlled.In the task orthogonal coordinate frame,the system dynamics is decoupled into tangential and normal directions,which represent contouring performance and advancing performance,respectively.In the task polar coordinate frame,the system dynamics is decoupled into radial and angular directions,which respectively represent contouring performance and advancing performance.The three-dimension contouring control problem then can be transformed into a two-dimension error regulation problem.Based on designing and tuning the contouring error and the advancing error controller,the contouring performance and the advancing performance can be controlled independently.Compared with traditional task coordinate frames,the establishment of proposed reduced-dimension task coordinate frames are not related to any specific contouring error estimation methods and only two sets of control parameters are needed for three-dimensional contouring control.Experiments on a three-axis CNC machine tool show validity and effectiveness of the proposed task orthogonal coordinate frame and the task polar coordinate frame.The computation cost for the proposed frames are respectively 18 microseconds and 20 microseconds,which are sufficient for real-time motion control.Since the commercial CNC system is blocked to apply dynamics control,the cross-coupled control is applied based on the single axis tracking control framework.In the original cross-coupled control structure,the calculation of cross-coupled gains is complicated.In this thesis,the cross-coupled gains are determined based on the direction cosine of the contouring error vector.Based on the proposed method,once the coordinates of contouring error are calculated,the cross-coupled gains can be determined easily and can be directly applied from two-dimension controls to three-dimension ones.The control program does not need any modification except the coordinates of contouring error position.Moreover,based on the separation of direction and magnitude of tracking error and contouring error,a modified cross-coupled control structure is proposed.Based on controlling tracking error magnitude and contouring error magnitude,the tracking performance and the contouring performance can be controlled separately.Based on the modified cross-coupled control structure,not only the calculation of cross-coupled gains can be simplified,but also designing and tuning of tracking controller and contouring controller can be simplified.