基于NURBS插补与等效误差法的直接驱动XY平台轮廓控制

摘要

为满足复杂型面零件的高速高精加工要求,采用造型功能强大的NURBS曲线插补的方法作为指定加工曲线的路径给定.对于由两台直线电机驱动的XY平台,系统的非线性、不确定因素以及曲线轨迹的轮廓误差模型相对复杂等问题影响其轮廓加工精度.采用适用于多轴非线性运动系统轮廓控制的等效误差法,建立可用于自由曲线跟踪且容易计算的XY平台等效误差非线性模型.为使采用等效误差法设计的控制器与NURBS插补路径给定兼容,采用Sylvester隐式化方法将NURBS曲线的参数形式转换为代数形式,从而将两者恰当的进行结合.综合使用两种方法设计二阶滑模控制器,在满足自由曲线加工的同时亦削弱了非线性因素的影响,使直线电机XY平台达到高精加工的要求.仿真结果表明,所设计的控制器能有效地提高XY平台的轮廓加工精度.%The Non Uniform Rational B-spline(NURBS) curve direct interpolator was investigated in detail aimed at the demand of complex profile parts' high speed and high accuracy CNC machining. The contour accuracy of XY table directly driven by two linear motors was influenced by the nonlinear dynamic, system uncertainties and complicated contour error model of curve trajectory. To establish XY table model that easily calculated and suitable for general curves, the equivalent errors method applicable for multi-axis nonlinear motion system was adopted. To combine the two method perfectly, Sylvester' s implicitization method is introduced to transform the parameter form of NURBS curve into algebraic representation. The controller is designed based on the integrated method, in order to satisfy the process of free-form curve and the reduction of the non-linear factor,thus achieve the accuracy requirements of XY table. Simulation results show that the designed control system of XY table has strong robustness and high contour accuracy.