多维超精密定位系统建模与控制关键技术研究

发布时间：2018-03-24 15:12

本文选题：迟滞非线性　切入点：Duhem模型　出处：《东南大学》2015年博士论文

【摘要】：精密定位技术是超精密加工技术、电子产品组装生产线、集成电路器件制造、生物工程及纳米技术等领域的关键性技术,纳米级定位技术作为纳米技术的一个主要研究方向,已成为各国研究的热点。纳米级定位技术中采用的致动器主要有微电机、压电(PZT)驱动器、形状记忆合金(SMA)驱动器等。压电陶瓷在超精密定位和微位移控制中具有其它驱动器无法比拟的优点,体积小、分辨率高、响应速度快等,是微位移技术中比较理想的驱动元件。但是,压电陶瓷驱动器具有严重的迟滞非线性特性,迟滞具有非光滑的多值映射特性,迟滞不仅会降低控制系统的精度,也会出现与激励信号幅值相关的相移及谐波失真现象,削弱控制系统的反馈作用,造成控制系统不稳定,严重影响压电陶瓷驱动器的广泛应用。为减小这种非线性特性所造成的不良影响,更好地发挥压电陶瓷的性能,很多科研机构和研究人员对压电超精密迟滞非线性系统建模与控制方面开展了相关研究。Duhem模型是一种由微分方程描述的迟滞模型,与Preisach模型相比,Duhem模型最大优点是具有明确的函数表达式,由一个参数a和两个函数f(·)、g(·)描述,能反映压电陶瓷的迟滞特性。由于Duhem模型是一种动态模型,使得模型输出与输入信号的速率相关,符合实际智能材料中迟滞非线性的动态特性。通过调整Duhem模型的参数α和两个函数f(·)、g(·)可以反映不同迟滞模型,因此,Duhem模型能够更精确的描述迟滞非线性。但是,Duhem模型中参数α和函数f(·)、g(·)很难选取,这也是Duhem模型应用的瓶颈。本文根据Weierstrass第一逼近定理,提出了应用多项式函数构造Duhem模型的函数f(·)和g(·),根据不同精度的要求,选取不同的阶次,解决Duhem模型函数及参数确定难的问题。采用递推最小二乘法,在线辨识Duhem模型的各个参数,并利用辨识结果方便快捷地建立了迟滞逆模型,避免了复杂的模型求逆过程,从而实现对压电超精密定位系统的自适应逆补偿控制。在德国PI公司的三维压电陶瓷执行平台上进行了测试,验证了该算法的有效性和正确性。超精密定位系统是由压电陶瓷作为驱动执行机构的装置,这样压电迟滞的输出成为不可直接测量的量,为系统的辨识带来不便。本文在分析模型的基础上,采用两步辨识方法,成功地解决这一难题。第一步,利用阶跃响应,辨识出线性部分参数。第二步,利用混合快速跟踪微分器设计出线性部分的逆函数,构成迟滞观测器,通过迟滞观测器有效观测出压电陶瓷迟滞输出。利用输入信号和观测值,辨识Duhem模型参数。成功地辨识出了超精密定位系统的模型参数,并利用逆补偿理论和反馈控制技术,实现了压电超精密平台的精密控制,通过实验验证了该方法的有效性。在多维超精密压电陶瓷运动定位系统中,不仅存在严重的非线性迟滞现象,也存在着轴间耦合现象,耦合现象严重影响控制系统的精度,同时也增加了控制器设计的难度。由于维间的耦合机理复杂,因素很多,难以从机理上对其建模,可以应用神经网络建立系统模型。由于迟滞是一对多的映射,因此,神经网络模型对于类似于迟滞非线性无能为力。根据迟滞的特性,本文给出扩展输入空间法构造迟滞算子的基本原则,根据该原则可以方便快捷构造出合适的迟滞算子,应用构造出的算子对神经网络的输入空间进行扩展,实现把原来的一对多映射转化成一对一或多对一映射关系,解决了神经网络不能建立迟滞类模型的问题。本文构造了一种新的动态迟滞算子,并证明了该算子可实现一对一的映射。为了选取最优参数采用遗传算法实现迟滞算子参数自动寻优。应用该算子建立了多维压电陶瓷执行器的迟滞正模型和逆模型。利用迟滞的正、逆模型,观测出多维系统中的维间输出耦合量,根据该观测值,应用前馈补偿实现了多维系统的解耦控制。本文从压电陶瓷的迟滞非线性入手,应用多项式逼近理论和辨识理论,成功应用Duhem模型描述了压电陶瓷的迟滞非线性,并采用两步辨识方法,辨识出由压电陶瓷构成的超精密定位系统的模型。针对该模型设计了迟滞逆补偿器和系统控制器,实验和实践效果良好。在一维的基础上,根据维间存在迟滞强耦合性特点,构造了一种新动态迟滞算子,扩展了输入空间,使得输入输出成为一一映射。利用神经网络建立了耦合系统的正、逆模型,应用该正逆模型设计了前馈控制器实现了维间的解耦控制,应用前馈-反馈控制技术,实现了多维超精密系统的解耦和控制,实验结果验证了该理论的正确性,该算法具有一定的实用价值和推广价值。
[Abstract]:Ultra precision machining technology is the precision positioning technology, electronic product assembly line, integrated circuit manufacturing, the key technology in the field of biotechnology and nanotechnology, nano positioning technology as a main research direction of nanotechnology, has become a hot point of research in the world. The nanometer positioning technique using the main actuator micro motor, piezoelectric actuator (PZT), shape memory alloy (SMA) actuators. Advantages of piezoelectric ceramic unmatched in ultra precision positioning and micro displacement control with other driver has the advantages of small volume, high resolution, fast response speed, is the ideal driving element in micro displacement technology. However, pressure electric actuator with hysteresis nonlinearity is serious, hysteresis with non smooth multi valued mapping of hysteresis characteristics, will not only reduce the precision of the control system, there will be associated with the exciting signal amplitude and phase Shift and harmonic distortion, weaken the feedback control system, the control system is not stable, widely used seriously affect the piezoelectric actuator. In order to reduce the adverse effects caused by the nonlinear characteristics, better performance of piezoelectric ceramics, many scientific research institutions and researchers of Ultra Precision Piezoelectric hysteresis nonlinearity system modeling and control study was carried out for a.Duhem model is described by differential equations of the hysteresis model, compared with Preisach model, Duhem model has the biggest advantage is the explicit function expressions, by a parameter a and two function f (-), G (-) description, can reflect the hysteresis of piezoelectric ceramics. The Duhem model is a dynamic model, the rate model of input and output signals related with dynamic characteristics of hysteresis in smart materials. Through the actual parameter adjustment of Duhem model And the two function f (-), G (-) can reflect the different hysteretic model, therefore, the Duhem model can describe the nonlinear hysteresis more accurate. However, the Duhem model parameter and function f (-), G (-) it is difficult to choose, which is the bottleneck for the application of Duhem model based on Weierstrass. The first approximation theorem, put forward the function application of polynomial functions to construct Duhem model of F (-) and G (-), according to the different accuracy requirements, selection of different order, solve the function and parameters of the Duhem model to determine the problem. By using recursive least squares method, the on-line parameter identification of Duhem model, and using the identification the results quickly established the inverse hysteresis model, avoiding the complex model of inverse process, so as to realize the inverse compensation control of adaptive piezoelectric ultra precision positioning system. In three pressure PI Germany's ceramic execution platform is tested, validate the algorithm The validity and correctness. Ultra precision positioning system is composed of piezoelectric ceramic actuator as the driving device, so that the output of piezoelectric hysteresis can not be directly measured, inconvenience of system identification. This paper based on the analysis of the model, using two step identification method, successfully solve this problem in the first step, the step response, identify the parameters of the linear part. The second step, mixed with fast tracking differentiator is designed the inverse function of the linear part, a hysteresis observer, through the observation of hysteresis observer effective piezoelectric hysteresis output. Using the signal input and observation value, parameter identification of Duhem model successfully identified. The model parameters of ultra precision positioning system, and using the inverse compensation theory and feedback control technology, to achieve the precision control of piezoelectric ultra precision platform, through experiments to verify the effectiveness of the method in multidimensional. Ultra Precision Piezoelectric Ceramic positioning system, not only the existence of nonlinear hysteresis phenomenon is serious, there is coupling between axes, coupling phenomenon seriously affect the precision of the control system, but also increase the difficulty of controller design. The coupling mechanism between the two dimensions is complex, due to many factors, it is difficult to the mechanism of the modeling. To establish the system model using neural network. The hysteresis is one to many mapping, therefore, the neural network model for similar to the hysteresis nonlinearity. According to the characteristics of hysteresis incapable of action, this paper gives the basic principle of expanded input space made hysteretic operator, according to the principle can be conveniently constructed suitable for hysteresis operator, operator application to construct the input space of the neural network expansion, to achieve the original one to many mapping into a one-to-one or many to one mapping relationship, solve the neural network To establish model hysteresis problem. This paper presents a new dynamic hysteresis model, and proves that the operator can achieve a one-to-one mapping. In order to select the optimal parameters by genetic algorithm operator parameter optimization automatically. The application of the operator set up a multi dimension piezoelectric ceramic actuators and hysteresis model the inverse model is used. The hysteresis, inverse model, the observation system of multidimensional inter dimensional output coupling, according to the observations, application of feedforward compensation decoupling control system. This paper from the multidimensional hysteresis nonlinearity of piezoelectric ceramics with the application of multivariate approximation theory and identification theory, the successful application of Duhem model the hysteresis nonlinearity of piezoelectric ceramics, and the two step identification method, identification of ultra precision positioning system model composed of piezoelectric ceramic. Designed for the model and the inverse hysteresis compensator controller, Experiment and practice good effect. On the base of one, according to the existing hysteresis coupling characteristics between dimensions, a dynamic hysteretic operator is constructed, expanded input space, the input and output of a one-to-one mapping. It, the inverse model of coupling system has been established by using the neural network, the application is a feedforward controller is designed to achieve the decoupling control between the dimension of inverse model, feedforward and feedback control technology application, realize the decoupling control of multidimensional ultra precision system, the experimental results verify the correctness of the theory, the algorithm has certain practical value and popularization value.

【学位授予单位】：东南大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TP273

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