光栅刻划机系统辨识及温度影响研究
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摘要
随着现代光谱技术的发展,光谱仪器在航空航天、天文观测、生物研究以及国防建设等各个领域都有广泛应用,而衍射光栅则是光谱仪器中的核心器件。光谱仪器的发展和进步与光栅制造技术水平息息相关。大行程高精度的衍射光栅必须采用机械式光栅刻划机进行制造,作为机械领域中最为精密的仪器之一,光栅刻划机结构复杂并且影响其精度的因素众多。本文对光栅刻划机的关键部件进行特性分析,对定位系统进行系统辨识研究,分析温度变化对光栅刻划机的影响规律,并在此基础上进行补偿系统研究。
光栅刻划机的主体结构包括定位系统、刻划系统以及测量系统,首先对这三个系统的具体结构以及光栅刻划机的工作方式进行详细介绍。然后对光栅刻划机的大行程定位和小行程定位的实验结果进行对比分析。为了提高光栅刻划机的性能,对其关键部件进行特性分析。分别对刻划系统中的复合刀架和刀架导轨以及定位系统中的工作台和工作台导轨进行模态分析和变形分析,再对粗定位系统和精定位系统进行理论建模,分析其系统稳定性等特性。
光栅刻划机的定位系统直接决定着光栅毛坯的位置,因此定位系统十分重要,为了分析定位系统的特性,对其进行系统辨识研究。对原始定位数据进行数据插补以及归一化处理后,采用两种方法进行系统辨识研究。第一种方法是基于ARX模型的系统辨识,根据实验数据先辨识模型的阶数再辨识模型的参数；第二种方法是基于理论模型的系统辨识,首先根据系统结构建立一个简化的动力学模型,然后在这个模型的基础上完成系统辨识。这两种辨识结果的对比结果表明,不同的辨识结果适用于不同的应用环境。
光栅刻划机作为一个纳米级精度要求的系统,环境温度变化对其精度也会造成一定的影响。为了研究温度变化对光栅刻划机精度的影响规律,首先采用有限元方法进行温度变形分析,然后再对温度-误差数据进行建模,采用了两种建模方式。其一是基于遗传算法的多项式建模,在参数迭代时使用了逐步优化方法计算最优的遗传算法参数；其二是基于广义回归神经网络的建模方法。建模结果验证了温度对光栅刻划机的影响是一个相对缓慢的过程。在此基础上建立温度补偿系统,采用了定常PID控制算法和单神经元PID控制算法,这两种控制算法都能有效补偿温度及其他因素对光栅刻划机精度的影响。采用了补偿结构的定位系统在环境温度为20+0.3℃时的定位精度高于未采用补偿结构的系统在环境温度为20±0.01℃时的定位精度。其中,单神经元PID控制算法由于其自适应性,控制精度相对更高。
The spectrum instruments are widely applied in the aerospace, astronomical observation, biology research, national defense construction, and so on. As the core component of the spectrum instrument, the diffraction grating directly affects the development of the spectrum instrument. Due to the requirements of large area and high precision, the grating must be manufactured by the mechanical grating ruling engine. The mechanism of the grating ruling is extremely complex. There are many factors that influence the accuracy. This paper analyzes the critical components of system and the characteristics of the positioning system are discussed based on the system identification. The relationship between the temperature vibration and the system error is researched and a compensation system has been built.
The mechanical grating ruling mainly includes the positioning system, the ruling system, and the measurement system. The detailed structure of the three systems and the working modes of the ruling engine are introduced. The positioning experiments of both the large travel mode and the short travel mode are conducted and compared. In order to understand the characteristics of the ruling engine, the core components are researched specially, including the positioning stage, the positioning guide rail, the tool holder, and the tool holder guide rail. The modal analysis and the deformation analysis are applied on the core components. The theoretical models of the coarse positioning system and the fine positioning system have been developed.
The grating is installed on the positioning stage. So the position of the positioning system directly affects the performance of the grating. The system identification of the positioning system is a practical method to learn the features. The preprocessing of the original data contains data interpolation and normalization processing. There are two different methods applied for system identification. The one is the method based on the ARX model. The model's order is determined firstly and the parameters of the ARX model are calculated secondly. The other method is the one based on the kinetic model. The kinetic model of the positioning system is built according to the real structure. Then the unknown parameters of the model are determined.
As an instrument with nanoscale precision, the grating ruling engine requires a very demanding environment. The temperature vibration will obviously impact the accuracy of the system. The temperature-error model is developed to research the relationship between the temperature vibration and the system error. Both the polynomial model based on the genetic neural network and the generalized regression neutral network is employed for modeling. On the basis of the temperature-error model, the compensation system has been developed. Two controllers are used in the system, the constant PID controller and the single neuron based PID controller. Both the two controllers can keep the accuracy of the ruling engine with the extended temperature range. The positioning precision of the ruling engine with compensation system and temperature range of20+0.3℃is higher than the one of the original system with temperature range of20±0.01℃. As an adaptive controller, the single neuron based PID controller is more adaptable than the constant PID controller.
光栅刻划机的主体结构包括定位系统、刻划系统以及测量系统,首先对这三个系统的具体结构以及光栅刻划机的工作方式进行详细介绍。然后对光栅刻划机的大行程定位和小行程定位的实验结果进行对比分析。为了提高光栅刻划机的性能,对其关键部件进行特性分析。分别对刻划系统中的复合刀架和刀架导轨以及定位系统中的工作台和工作台导轨进行模态分析和变形分析,再对粗定位系统和精定位系统进行理论建模,分析其系统稳定性等特性。
光栅刻划机的定位系统直接决定着光栅毛坯的位置,因此定位系统十分重要,为了分析定位系统的特性,对其进行系统辨识研究。对原始定位数据进行数据插补以及归一化处理后,采用两种方法进行系统辨识研究。第一种方法是基于ARX模型的系统辨识,根据实验数据先辨识模型的阶数再辨识模型的参数；第二种方法是基于理论模型的系统辨识,首先根据系统结构建立一个简化的动力学模型,然后在这个模型的基础上完成系统辨识。这两种辨识结果的对比结果表明,不同的辨识结果适用于不同的应用环境。
光栅刻划机作为一个纳米级精度要求的系统,环境温度变化对其精度也会造成一定的影响。为了研究温度变化对光栅刻划机精度的影响规律,首先采用有限元方法进行温度变形分析,然后再对温度-误差数据进行建模,采用了两种建模方式。其一是基于遗传算法的多项式建模,在参数迭代时使用了逐步优化方法计算最优的遗传算法参数；其二是基于广义回归神经网络的建模方法。建模结果验证了温度对光栅刻划机的影响是一个相对缓慢的过程。在此基础上建立温度补偿系统,采用了定常PID控制算法和单神经元PID控制算法,这两种控制算法都能有效补偿温度及其他因素对光栅刻划机精度的影响。采用了补偿结构的定位系统在环境温度为20+0.3℃时的定位精度高于未采用补偿结构的系统在环境温度为20±0.01℃时的定位精度。其中,单神经元PID控制算法由于其自适应性,控制精度相对更高。
The spectrum instruments are widely applied in the aerospace, astronomical observation, biology research, national defense construction, and so on. As the core component of the spectrum instrument, the diffraction grating directly affects the development of the spectrum instrument. Due to the requirements of large area and high precision, the grating must be manufactured by the mechanical grating ruling engine. The mechanism of the grating ruling is extremely complex. There are many factors that influence the accuracy. This paper analyzes the critical components of system and the characteristics of the positioning system are discussed based on the system identification. The relationship between the temperature vibration and the system error is researched and a compensation system has been built.
The mechanical grating ruling mainly includes the positioning system, the ruling system, and the measurement system. The detailed structure of the three systems and the working modes of the ruling engine are introduced. The positioning experiments of both the large travel mode and the short travel mode are conducted and compared. In order to understand the characteristics of the ruling engine, the core components are researched specially, including the positioning stage, the positioning guide rail, the tool holder, and the tool holder guide rail. The modal analysis and the deformation analysis are applied on the core components. The theoretical models of the coarse positioning system and the fine positioning system have been developed.
The grating is installed on the positioning stage. So the position of the positioning system directly affects the performance of the grating. The system identification of the positioning system is a practical method to learn the features. The preprocessing of the original data contains data interpolation and normalization processing. There are two different methods applied for system identification. The one is the method based on the ARX model. The model's order is determined firstly and the parameters of the ARX model are calculated secondly. The other method is the one based on the kinetic model. The kinetic model of the positioning system is built according to the real structure. Then the unknown parameters of the model are determined.
As an instrument with nanoscale precision, the grating ruling engine requires a very demanding environment. The temperature vibration will obviously impact the accuracy of the system. The temperature-error model is developed to research the relationship between the temperature vibration and the system error. Both the polynomial model based on the genetic neural network and the generalized regression neutral network is employed for modeling. On the basis of the temperature-error model, the compensation system has been developed. Two controllers are used in the system, the constant PID controller and the single neuron based PID controller. Both the two controllers can keep the accuracy of the ruling engine with the extended temperature range. The positioning precision of the ruling engine with compensation system and temperature range of20+0.3℃is higher than the one of the original system with temperature range of20±0.01℃. As an adaptive controller, the single neuron based PID controller is more adaptable than the constant PID controller.
引文
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金海薇.2011.基于ARX模型的齿轮箱建模方法[J].振动与冲击,30：230-233.
李燕青,郝德阜.2003.衍射光栅制造技术的发展[J].长春理工大学学报,26：66-68.
李志农,何永勇,吴昭同,等.2006ARMA模型盲辨识仿真研究及其在机械故障诊断中的应用[J].振动与冲击,25：122-124.
时轮,郝德阜,齐向东.2001.高精度的光电式衍射光栅刻划机[J].仪器仪表学报,2(4)：103-104
徐向东,洪义麟,傅绍军,等,2004,全息离子束刻蚀衍射光栅[J],物理,5：340-344
孙禹,徐克林,秦玮.2011.基于广义回归神经网络的工程公司风险评估[J].工业工程,14：119-123
于开平,牟晓明.2010.基于前向神经网络的非线性时变系统辨识改进EKF算法[J].振动与冲击,29：5-8.
Cao Y, Chen XB.2012. A novel discrete ARMA-based model for piezoelectric actuator hysteresis [J]. ASME Transactions on Mechatronics,17:737-744
Chang SH, Du BC.1998. A precision piezodriven micropositioner mechanism with large travel range. Rev Sci Instrum,69(4):1785-91
Chang SH, Li SS.1999. A high resolution long travel friction-drive micropositionger with programmable step size [J]. Rev Sci Instrum,70:2776-2782
Cheng F, Fan KC, Miao JW, Li BK, Wang HY.2012. A BPNN-PID based long-stroke nanopositioning control scheme driven by ultrasonic motor [J]. Precis Eng,36:485-493
Chen CL, Jang MJ, Lin KC.2004. Modeling and high-precision control of a ball-screw-driven stage [J]. Precis Eng,28:483-485
Chen X, Wang N.2010. Modeling a delayed coking process with GRNN and double-chain based DNA genetic algorithm [J]. International Journal of Chemical Reactor Engineering,8:A75
Chu CL, Fan SH.2006. A novel long-travel piezoelectric-driven linear nanopositioning stage [J]. Precis Eng,30:85-95
Dudnikov VG, Kovalevsky DV, Shabalin AL.1991. Simple, high preci-sion linear-motor-driven XYθ positioner (Walker). Rev Sci Instrum,62(10):2492
Eastwood S, Webb P.2009. Compensation of thermal deformation of a hybrid parallel kinematic machine [J]. Robot Cim-Int Manuf,25:81-90
Erwin G, Loewen, Robert S, Wiley. Large diffraction grating ruling engine with nanometer digital control. system.Proc. SPIE,815:88-98,1987.
Fan KC, Chu CL, Chang SH, Chung TT.2001. Development of a micro-CMM for nanometrology. Keynote Paper, Proceedings of the Spring Conference KSPE, Korea,3-7.
Fan KC, Lai ZF.2008. An intelligent nano-positoning control system driven by an ultrasonic motor [J].Int J Precis Eng Man,9:40-45
Fan KC.2007. An intelligent thermal error compensation system for CNC machining Centers [J]. J Chin Soc Mech Eng,28:91-97
Flores JJ, Graff M, Rodriguez H.2012. Evolutive design of ARMA and ANN models for time series forecasting [J]. Renewable Energy,44:225-230.
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