高速、高精度数控机床位置伺服系统一直存在强耦合、非线性等问题，该类问题会产生较大的跟踪误差及轮廓误差，目前大多数控制算法仅考虑了单轴的跟踪误差补偿，通过提高单轴控制精度来间接提高轮廓加工性能，而对轮廓误差的控制不够重视。目前轮廓误差控制的问题来自于现有的轮廓误差估计模型精度不够，大多采用严重依赖跟踪误差的估计模型，没有直接对轮廓误差进行闭环控制。针对以上问题，提出一种改进的轮廓误差估计及控制方案并进行理论分析和实验验证，具体工作如下：

对数控机床二维轮廓误差来源和现有轮廓误差估计方法进行分析。提出了一种基于牛顿搜索算法的直接轮廓误差估计方法，并对其收敛性进行证明，与现有方法进行轮廓误差估计精度的对比分析。该方法以机床当前实际加工位置与伺服系统给定位置为输入量，直接进行轮廓误差的估计计算，将轮廓误差估计归类为优化问题，设置一个损失函数进行搜索，找到轮廓误差的最优结果，解决使用跟踪误差进行间接计算造成累计误差的问题。

通过分析现有二维轮廓误差交叉耦合控制原理及缺陷，提出改进的交叉耦合控制框架，以轮廓误差分量与跟踪误差叠加作为控制器的输入量，位置控制器将常规PID算法与单神经元算法相结合，引入模糊控制理论对单神经元输出增益系数进行整定，设计单神经元模糊PID控制器替代原有的PID控制器。通过仿真实验，对比分析单神经元模糊PID控制器与常规PID控制器在单轴控制和轮廓控制中的表现，结果表明，单神经元模糊PID控制器优于常规PID控制模型，改进的交叉耦合控制方法优于现有的交叉耦合算法，呈现出较好的轮廓误差控制效果。

为了获取数控机床准确的坐标位置，对电机编码器信号进行倍频处理，利用编码器输出信号为正余弦信号的特点，设计幅值分割细分方法对其进行角度分割，选用Xilinx Spartan-6系列的FPGA芯片XC6SLX25T进行位置检测模块的实验验证，最后获得120倍分辨率的输出信号，提高数控机床位置检测精度，进而可提高轮廓误差的估计精度和控制精度。

本文的实验平台为XY二维运动控制平台，运动控制器选用DSP+FPGA+PC架构，完成器件选型及电路设计；在CCS6.0软件环境下编写控制程序并进行仿真调试，实现XY坐标轴的运动控制功能。最后，给定正圆轮廓、抛物线轮廓以及四角星型轮廓进行加工，验证改进算法的轮廓误差控制效果。实验结果表明单神经元模糊PID控制器优于常规PID控制器，响应更快，跟踪性能更好；改进的交叉耦合方法与现有的交叉耦合方法相比，能显著地减小轮廓误差，在加工圆弧和尖锐角度时，均能展现良好的轮廓加工性能。

The position servo system of high-speed and high-precision CNC machine tools is always restricted by the problems of coupling and nonlinearity. Tracking error and contour error are caused by this kind of problem. At present, only single-axis tracking error compensation is considered to improve indirectly the contour processing performance in most control algorithms, and then the control of contour error is neglected. At present, the problem of contour error control is that the precision of existing contour error estimation model is not accurate enough. The existing estimation model which relies on tracking error has no direct closed-loop control for contour error. To solve the above problems, an improved contour error estimation and control scheme is proposed and verified by theoretical analysis and experiments. The specific work is as follows:

The causes of two-dimensional contour error of CNC machine tools and the existing methods of contour error estimation are analyzed. A direct contour error estimation method based on Newton search algorithm is proposed and its convergence is proved. The contour error estimation accuracy of the proposed method is compared with that of the existing methods. In this method, the actual machining position of the machine tools and the given position of the servo system are taken as the input of the system to calculate directly the contour error. The contour error estimation is classified as an optimization problem.. In the improved method, the loss function is set to search the result, and the optimal result of the contour error is obtained. Therefore, the problem of contour error being indirectly calculated by tracking error is solved. 

The existing two-dimensional contour error cross-coupling control principle and defects are analyzed, and an improved cross-coupling control framework is proposed. Firstly, the contour error component and the tracking error are added as the input of the controller. Secondly, the conventional PID algorithm is combined with the single neuron algorithm. Fuzzy control theory is introduced to adjust the output gain coefficient of single neuron. Finally, the conventional PID controller is replaced by single neuron fuzzy PID controller. Through simulation experiments, the performance of single neuron fuzzy PID controller and conventional PID controller in single axis control and contour control are compared and  analyzed. The simulation results show that the single neuron fuzzy PID controller is better than the conventional PID control model. It is shown that the improved cross-coupling control method has better contour error control effect and is better than the existing cross-coupling algorithm.

In order to obtain the precise coordinate position of CNC machine tools, the motor encoder signal is subdivided. The output signal of the encoder is a sine-cosine signal, and based on this characteristic, the subdivision method of amplitude division is designed. The Xilinx Spartan-6 series FPGA chip XC6SLX25T is selected for the experimental verification of position detection module. The output signal with 120 times resolution is obtained by this method, which means the position detection precision of CNC machine tool is improved, and the contour error estimation precision and control precision are improved.

In this paper, the experimental platform is XY two-dimensional motion control platform, and the DSP + FPGA + PC architecture is selected as the hardware scheme of the motion controller. Under the CCS6.0 software environment, the control program has been written and debugged, and the motion control function of the XY coordinate axis has been realized. Finally, the contour error control effect of the improved algorithm is verified by the given processing of the circle contour, the parabola contour and the star contour. The experimental results show that the single neuron fuzzy PID controller has faster response performance and better tracking performance than the conventional PID controller. Compared with the existing cross-coupling method, the contour error can be reduced by the improved cross-coupling method. When machining circular arc and sharp angle, the good contour machining performance is shown by the improved method.

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