测量时延在线估计与批间控制器协同设计

批间控制是半导体批次生产过程中常用算法,其关键问题在于能够及时获取上一批次的制程输出,受测量手段及其成本限制,实际的生产制程很难满足这一要求.为此,本文提出一种基于贝叶斯统计分析的测量时延估计算法.在分析晶圆质量与实测时延、估计时延、以及制程漂移之间的逻辑关系的基础上,并将晶圆的质量信息按加工时间顺序划分两个相邻的滚动时间窗口.基于贝叶斯后验概率函数,及时捕获后一个滚动时间窗口内过程输出发生漂移的概率,从而判断是否有测量时延发生,并估算该时延大小.在此基础上,给出批间控制器的测量时延补偿策略,及时调整制程的控制量,提高晶圆的加工品质.仿真结果验证所提出算法的有效性.     

间歇生产过程的R调节学习控制

针对间歇生产过程迭代学习控制难以进行跟踪性能分析的难题,本文提出一种变R调节迭代学习控制算法,借鉴经典控制理论定义有界跟踪和零跟踪概念.以此研究能够让系统输出误差达到零跟踪的迭代学习控制策略,并严格地证明了算法的性能,得出可以通过调节权值R使过程产品质量的误差收敛到与模型精度相关联的有界区域的结论,为相关理论结果实施于实际间歇过程提供了理论依据.     

电阻点焊的变论域模糊控制方法

为提高电阻点焊模糊控制适应性和稳定性差的缺点, 根据变论域控制理论, 提出了电阻点焊的变论域模糊控制方法. 首先, 讨论了变论域模糊控制的基本原理. 其次, 设计了输入隶属函数、输出隶属函数、模糊控制规则、伸缩因子, 开发了一种基于规范化因子的电阻电焊变论域模糊控制器, 并使用模糊规则选择变论域的伸缩因子,给出了算法实现的具体步骤. 最后, 进行了不同控制方案的实验研究, 分析了实验结果, 验证了该控制算法的优越 性.     

高阶PID采样迭代学习控制

针对一类非线性带扰动系统提出了高阶PID采样速代学习控制算法,讨论了高阶算法的收敛性问题以及该算法的优势与缺陷.与传统的证明方法不同,利用泰勒级数展开法证明了被控对象在输入干扰和输出测量噪声均有界的情况下,高阶PID采样速代学习控制算法的收敛性,并且得出了收敛条件.由于收敛条件中没有积分项,因此更加利于分析计算.与传统的一阶采样迭代学习控制算法相比,高阶采样迭代学习控制算法由于利用了更多先前的控制信息而能使被控对象的实际输出更加接近理想输出.给出了相应的数值仿真,证明了理论分析的有效性.与此同时,结合啤酒生产过程中糖化阶段中酒花添加等实际问题对该算法的应用前景作了一定的分析.     

基于FTC的BBMC调速控制策略及参数优化

针对以Buck-boost矩阵变换器(BBMC)为功率变换器的异步电机调速系统, 提出一种基于有限时间控制(FTC)的变频调速控制方法.首先根据异步电机的给定转速, 经基于PI-IP控制的矢量控制算法获得BBMC的参考输出电压; 再以BBMC中电容电压与电感电流作为系统控制变量, 经有限时间控制算法得到BBMC中对应功率开关的占空比; 再根据该占空比对BBMC中对应功率开关实施控制, 即可在BBMC输出端获得与其参考输出一致的输出电压, 从而实现异步电机实际转速对其给定转速的准确跟踪, 达到对异步电机转速进行准确控制的目的; 同时采用自适应狼群优化算法对BBMC主电路参数及基于有限时间的控制参数进行优化, 取得了满意的效果.最后通过仿真和实验对上述控制方法进行了验证.     

融合闭环反馈机理的多变量预测控制策略

针对在模型预测控制中模型失配较严重时,单独使用动态矩阵控制不能满足控制需要的问题,提出了融合闭环反馈机理的多变量预测控制策略.讨论了多输入多输出系统中输入和输出的配对问题,以及控制算法中的PID控制强度问题,在动态矩阵控制的基础上引入PID反馈,利用动态矩阵控制算法的鲁棒性强及PID控制算法抗干扰性能好的优点,极大地弥补了模型失配的影响.通过对一个经典两输入两输出控制问题的仿真,表明该控制策略具有明显优于单独的DMC控制的性能.     

非线性系统迭代跟踪控制的批次遗忘学习算法

针对P型迭代学习算法对初始偏差和输出误差扰动敏感,以及PD型迭代学习算法容易放大系统噪声,降低系统鲁棒性的问题,研究了具有任意有界扰动及期望输出的重复运行非线性时变系统的PD型迭代学习跟踪控制算法.利用迭代学习过程记忆的期望轨迹、期望控制以及跟踪误差,给出基于变批次遗忘因子的学习控制器设计,并借助λ范数理论和Bellman-Gronwall不等式,讨论保证闭环跟踪系统批次误差有界的学习增益存在的充分必要条件,及分析控制算法的一致收敛性.本算法改善了系统的鲁棒性和动态特性,单关节机械臂的跟踪控制仿真验证了方法的有效性.     

基于广义混杂预测算法的智能车电机控制

智能汽车的关键技术在于根据传感器获取的道路输入信息确定汽车转角及速度的输出。针对广义预测控制算法(GPC)对离散系统控制的局限性,结合混杂动态逻辑模型(MLD)以及广义预测算法的特点,提出一种广义混杂预测控制算法。该算法主要利用在被控对象的数学模型中引入辅助二进制变量,在不影响系统稳定性的前提下,增加了对离散事件的响应,扩展了广义预测控制算法在混杂系统中的应用。以飞思卡尔智能车模为控制对象,对电机的控制算法进行了实际测试。实验结果表明,该算法自适应能力强,稳定度高,可以实现智能车模型的平稳快速过弯。     

EAST垂直位移快速控制的模拟与输出优化

EAST(Experimental Advanced Superconducting Tokamak)等离子体垂直位移快速控制系统在保障等离子体平稳运行、获得高性能等离子体方面起到重要的作用。目前EAST垂直位移控制算法集成在等离子体控制系统PCS(Plasma Control System)中,利用反射内存卡将控制命令传输到快控电源从而进行控制,这种方案具有较长的系统间通信延迟以及输出读写延迟。基于PCS中控制算法,设计一套独立的垂直位移控制算法,使得系统从PCS中剥离,减少系统通信延迟,并提出一种算法模拟方案,利用历史数据实现算法模拟。同时引入一种新型输出机箱替代原有的输出方式,通过光纤传输,缩短输出延迟,提高系统响应速度,满足控制需求。     

一类具有漂移、扩散及停时的奇异型随机控制

以随机分析的知识和最优控制理论为基础,推广了一类带停时的奇异型随机控制中的折扣费用模型,主要在受控状态过程中增加了漂移因子和扩散因子,使其为一随机微分方程的解,并将费用函数一般化.通过求解一组变分方程,证明了最优控制及最优停时的存在性,并给出了最优费用函数的解析表达式.     

Coordination and control of batch-based multistage processes

Run-to-run (R2R) process control has attracted much attention in research and has been widely used in practice. It has been proved effective at compensating for process disturbances by using R2R controllers at a single stage. However, most manufacturing processes span across multiple stages; variation in earlier stages can be magnified stage by stage if they are not properly eliminated. In addition, products are processed batch by batch in certain manufacturing processes. In such cases, the traditional EWMA controller might not effectively reduce the variation. This paper focuses on developing a process control strategy for batch production in a multistage process. In the newly proposed framework, a batch-allocation operation is introduced to group products into similar clusters before each stage; an R2R controller is then implemented to generate customized recipes for each batch. This framework emphasizes better coordination among the stages in a multistage process. Simulation results show that the proposed strategy is effective for the reduction of variation.     

Multiple-input multiple-output double exponentially weighted moving average controller using partial least squares

This paper applies the partial least squares (PLS) method to the multiple-input multiple-output (MIMO) semiconductor processes in the run-to-run (R2R) control practice. Due to the property of batch processing, the semiconductor manufacturing processes frequently exhibit high multicollinearity among input variables and dependency among output variables. These two effects will typically cause variance inflation of the regression coefficient estimates which are utilized in triggering or updating the R2R controller. Furthermore, the process nonlinearity is also likely to occur in some semiconductor processes. As the nonlinearity exists, the performance of the exponentially weighted moving average (EWMA) controller is not adequate and becomes aggravated after a few transient runs. The PLS method is, essentially, well suited for situations where multicollinearity is present among input variables. To rectify the aforementioned difficulties that might realistically take place in practice, the PLS method is considered in this paper a potential estimation alternative to the standard regression method. Three types of R2R simulation studies are conducted to verify the advantages of the PLS method. The simulation results show that using the PLS method as the model-building technique helps the EWMA controller to yield more consistent and robust control outputs than purely using the conventional EWMA controller.     

Evaluation of fuzzy neural network run-to-run controller using numerical simulation analysis for SISO process

During the past decade, a variety of run-to-run (R2R) control techniques have been proposed and extensively used to control various semiconductor manufacturing processes. The R2R control methodology combines response surface modeling, engineering process control, and statistical process control, with the main objective of fine-tuning the recipe so that the process output of each run can be maintained as close to the nominal target as possible. In this paper, the single-input single-output (SISO) model is addressed. To overcome the shortcomings in the traditional R2R EWMA controller, a fuzzy neural network (FNN) control strategy is proposed. When a process has large autoregressive parameters, traditional EWMA control methods cannot establish stable SISO process control. To solve this problem, an SISO process control model based on an FNN was used to build an SISO process control procedure. The analysis results from a numerical simulation indicated that when the coefficient of autocorrelation  > 0.6, the MSE ratio when using the FNN controller was 97.11% lower than when using the EWMA controller and 61.12% lower than when using an adaptive EWMA controller. This showed that the FNN control method established better SISO process control than the EWMA and adaptive EWMA control methods.     

含随机测量时延的EWMA批间控制器设计

批间控制(RtR)是半导体晶圆生产过程控制的有效算法. 然而, 受测量手段与测量成本的限制, 难以实时检 测晶圆的品质数据, 即: 存在一定的测量时延, 通常该测量时延是随机, 时变的, 且直接影响批间控制器的性能. 为 此, 本文基于指数加权移动平均(EWMA)算法, 提出一种含随机测量时延的扰动估计方法. 在分析测量概率的基础 上, 建立包含测量时延概率的扰动估计表达式; 并采用期望最大化(EM)算法估计该测量时延的概率; 然后分析系统 可能存在的静差项, 给出相应的补偿算法; 最后讨论系统的稳定性. 仿真实例验证所提算法的有效性.     

Stability analysis and optimal tuning of EWMA controllers – Gain adaptation vs. intercept adaptation

Exponentially weighted moving average (EWMA) controllers are the most commonly used run-to-run controllers in semiconductor manufacturing industry. An EWMA controller can be implemented in two different ways. One way is to keep the process gain as its off-line estimate and update the intercept term at each run, which is termed EWMA with intercept adaptation; the other is to keep the intercept term as its off-line estimate and update the process gain at each run, which is termed EWMA with gain adaptation. Despite the fact that gain variation and adaptation is typical in semiconductor industry, most EWMA formulations are for intercept adaptation and few results exist on the stability and sensitivity of EWMA with gain adaptation. In this paper, we propose a general formulation to analyze the stability of both EWMA controllers. The proposed state-space representation not only reveals the similarities and differences between two types of EWMA controllers, but also explains why the stability conditions for both types of EWMA controllers are independent of process disturbances. In addition, we propose a general framework that unifies the analysis of the optimal control performance for both types of EWMA controllers. The proposed framework is different from existing approaches in that it decouples the state estimation from the control law, and derives the optimal weighting based on the state estimation performance. The proposed framework significantly simplifies the analysis procedure, especially for EWMA with gain adaptation. Using this framework, we derive the optimal EWMA weighting through solving the discrete-time algebraic Riccati equation (DARE) for various process disturbances that are encountered in semiconductor manufacturing industry. Simulation examples are given to illustrate the optimality of the EWMA weighting derived using the framework. Some practical aspects of controller tuning are also discussed based on the simulation results.     

A Kalman filter-based R2R control system with parallel stochastic disturbance models for semiconductor manufacturing processes

A Kalman filter-based run-to-run control system has been proposed for minimum variance control of semiconductor manufacturing process. In the proposed control system, both gain- and bias-varying process models combined with different stochastic disturbance models were considered and identified in parallel. The best-fit model is selected and used for the R2R controller design. Sub-models of the ARIMA(1,1,1) process were considered for stochastic modeling of the bias and gain variation, and the Kalman filters are used to find the optimum model parameter estimation. The control performance was analyzed for each case of the disturbance model to investigate the expected benefit from the control system in comparison with the EWMA filter-based controller.     

A multivariate control chart for simultaneously monitoring process mean and variability

Recently, monitoring the process mean and variability simultaneously for multivariate processes by using a single control chart has drawn some attention. However, due to the complexity of multivariate distributions, existing methods in univariate processes cannot be readily extended to multivariate processes. In this paper, we propose a new single control chart which integrates the exponentially weighted moving average (EWMA) procedure with the generalized likelihood ratio (GLR) test for jointly monitoring both the multivariate process mean and variability. Due to the powerful properties of the GLR test and the EWMA procedure, the new chart provides quite robust and satisfactory performance in various cases, including detection of the decrease in variability and individual observation at the sampling point, which are very important cases in many practical applications but may not be well handled by existing approaches in the literature. The application of our proposed method is illustrated by a real data example in ambulatory monitoring.     

A G&P EWMA algorithm for high-mix semiconductor manufacturing processes

In mixed run processes, typical in semiconductor manufacturing and other automated assembly-line type process, products with different recipes will be produced on the same tool. Product based run-to-run control can be applied to improve the process capability. The effect of product-based controller on low frequency products is, however, minimal, due to inability to track tool variations. In this work, we propose a group and product based EWMA control scheme which combines adaptive k-means cluster method and run-to-run EWMA control to improve the performance of low frequency products in the mixed run process. Similar products could be classified into the same group adaptively and controlled by a group EWMA controller. The group controller is updated by both low frequency products and similar high frequency products; so that low frequency products can be improved by shared information from similar large frequency products. However, the high frequency products are controlled by individual product-based EWMA to avoid interference of the low frequency products. The advantages of proposed control scheme are demonstrated by benchmark simulation and reversed engineered industrial applications.     

Cycle forecasting EWMA (CF-EWMA) approach for drift and fault in mixed-product run-to-run process

In semiconductor manufacturing processes, mixed-products are usually fabricated on the same set of process tool with different recipes. Run-to-run controllers which based on the exponential weighted moving average (EWMA) statistic are probably the most frequently used in industry for the quality control of certain semiconductor manufacturing process steps. However, for mixed-product drifted process, if the break length of a product is large, then the process output at the beginning runs of each cycle will far deviate from the target value which will lead to a possible high rework rate and lots of waste wafers. Therefore, this study aims to develop a new approach named cycle forecasting EWMA (CF-EWMA) approach to deal with the problem of large deviations in the first few runs of each cycle. Furthermore, a common fault, i.e., the step fault, is also considered in this paper, and fault tolerant cycle forecasting EWMA (FTCF-EWMA) approach is proposed. Simulation study shows that the proposed approaches are effective.     

Analytic network process decision-making to assess slicing machine in terms of precision and control wafer quality

We discuss and develop a manufacturing quality yield model to forecast the 12 in silicon wafer slicing based on an analytic network process (ANP) framework. The ANP is a general theory of relative measurement used to derive composite-priority-ratio scales from individual-ratio scales that represent the relative influence of factors that interact with respect to the control criteria. Through its supermatrix, which is composed of matrices of column priorities, the ANP framework captures the outcome of dependence and feedback within and between clusters of factors. Additionally, the proposed algorithm can select the evaluation outcomes to identify the optimal machine of precision. Finally, results of the EWMA control chart and Process Capability Indices demonstrate the feasibility of the proposed ANP-based algorithm in effectively selecting the evaluation outcomes and in evaluating the precision of the optimal performing machines. We illustrate how the ANP model implemented for helping the engineer can find out the manufacturing process yield quickly and effectively.