光刻机工件台前馈补偿器参数整定方法  

Parameter tuning of the wafer stage compensation feedforward controller of the lithography machine

作　　者：刘涛[1] 杨开明[1] 朱煜[1] LIU Tao;YANG Kaiming;ZHU Yu(Beijing Key Laboratory of Precision/Ultra-Precision Manufacturing Equipment and Control,State Key Laboratory of Tribology,Department of Mechanical Engineering,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学机械工程系,摩擦学国家重点实验室,精密超精密制造装备及控制北京市重点实验室,北京100084

出　　处：《清华大学学报（自然科学版）》2023年第10期1640-1649,共10页Journal of Tsinghua University(Science and Technology)

基　　金：国家科技重大专项(2017ZX02102004)。

摘　　要：前馈控制器是光刻机工件台在高加减速工况下实现纳米级运动精度的关键环节。该文针对传统情况下四阶前馈拟合逆模型能力较差、难以完全消除参考轨迹导致重复性误差的问题,提出了一种以四阶前馈为基础,外加有理分式补偿器的前馈控制架构,并针对该有理分式补偿器控制参数整定的问题,提出了一种数据驱动的参数整定方法。该方法利用系统辨识的相关规则,将前馈补偿器参数整定过程的非凸优化问题转化为凸优化问题,进而给出了全局最优参数整定方法以及参数迭代过程中梯度、Hessian矩阵的无偏估计方法;通过光刻机工件台的实验验证了所提参数整定方法具有收敛性。实验结果表明:所提出的补偿前馈能够有效消除四阶前馈未消除的残余误差。[Objective]The feedforward controller is crucial to achieving nano-level motion accuracy for the lithography wafer stage under high acceleration and deceleration conditions.Traditional 4-order feedforward is widely used to control precision motion systems because of its intuitive physical meaning and simple parameter tuning.However,its capacity to fit the inverse model is inadequate,and it is difficult to eliminate the repetitive error caused by the input trajectory.Therefore,a feedforward control architecture using the 4-order feedforward and an extra rational fraction compensator is proposed.[Methods]In this study,the input signal of the compensator is the higher-order derivative of the reference trajectory,and the numerator and denominator of the compensator use the delay unit as the basis function.Therefore,obtaining the unknown parameters of the basis function is crucial to the design.This paper proposes a data-driven iterative parameter tuning strategy for the compensation controller.The difficulty is that the tuning problem is a nonconvex optimization problem,making global parameter optimization challenging.This paper uses the relevant rules of system identification to address the issue at hand.The purpose of adding compensatory feedforward is to eliminate the residual error after using the 4-order feedforward,which is equivalent to achieving a zero-generalized error.Since the generalized error has a linear connection with the compensator parameters,the original nonconvex optimization problem is successfully transformed into a convex problem by minimizing the 2-norm of the generalized error.Through the above transformation,the global optimal point is obtained by the Gauss—Newton method,and the step size condition for ensuring iterative convergence is provided.In addition,the gradient and Hessian matrix of the objective function need to be incorporated into the parameter updating law,even though their exact values are difficult to obtain.This paper derives their unbiased estimates using two impulse respon

关 键 词：前馈控制 有理前馈控制器 补偿前馈 数据驱动 参数整定 工件台 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]