面向压电陶瓷纳米驱动平台的先进控制器设计

发布时间：2018-11-05 07:23

【摘要】：纳米技术是一项在各个方面改变人类生产生活方式的革命性科学技术,已经广泛应用在人类生活各个领域。纳米定位技术是实现纳米技术应用的基础,压电陶瓷位移驱动器可以实现纳米级的位移,但是磁滞等非线性特性的存在会极大地影响其跟踪和定位性能。本文将从三个不同的角度来研究压电陶瓷磁滞的补偿问题,首先使用经典的基于模型的控制方法：根据压电陶瓷的输入输出数据,使用Prandtl-Ishlinkii模型对磁滞进行建模。为了弥补经典的Prandtl-Ishlinkii模型与实际磁滞之间的差异,在经典Prandtl-Ishlinkii模型的基础上引入新的算子,得到改进的Prandtl-Ishlinkii模型。根据得到的磁滞模型推导出逆模型,依据恒等映射的原理使用逆模型对系统进行线性化,进而采用传统的控制器设计的方法,对线性化后的系统设计反馈控制器以补偿建模误差。考虑到磁滞建模过程的复杂性,接下来将一种全新的L1自适应控制算法应用在压电陶瓷的磁滞补偿问题中,从而省去了传统方法中磁滞建模的复杂过程。压电驱动系统被分解为一个磁滞子系统和线性动态子系统,磁滞子系统的输出作为线性动态子系统的输入。磁滞经过变换,转化为线性系统的扰动,然后使用L1自适应控制算法进行处理。经过理论推导,证明了系统的稳定性。在实验中与比例-积分-微分(PID)控制器进行对比,得到了更好的控制效果,从而验证了控制算法的有效性。最后结合前面两种方法的优点,采用了基于Prandtl-Ishlinkii模型的L1自适应控制算法。仍然采用解耦的结构对系统进行描述,使用Prandtl-Ishlinkii模型对磁滞进行转换,相比于单独使用L1自适应控制器,此时不仅能够减少L1自适应控制器中不确定参数的个数,同时也缩小了不确定参数的变化范围,有利于进一步减小控制误差。
[Abstract]:Nanotechnology is a revolutionary technology to change the way of life and production of human beings in all aspects. It has been widely used in all fields of human life. Nano-localization technology is the basis for the application of nano-technology. Piezoelectric ceramic displacement actuator can achieve nano-level displacement, but the existence of nonlinear characteristics such as hysteresis will greatly affect its tracking and positioning performance. In this paper, the compensation of hysteresis of piezoelectric ceramics is studied from three different angles. Firstly, the classical model-based control method is used: according to the input and output data of piezoelectric ceramics, the Prandtl-Ishlinkii model is used to model the hysteresis. In order to make up for the difference between the classical Prandtl-Ishlinkii model and the real hysteresis, a new operator is introduced on the basis of the classical Prandtl-Ishlinkii model, and an improved Prandtl-Ishlinkii model is obtained. According to the obtained hysteresis model, the inverse model is derived, and the inverse model is used to linearize the system according to the principle of identity mapping, and then the traditional controller design method is adopted. A feedback controller is designed to compensate the modeling error for the linearized system. Considering the complexity of hysteresis modeling, a novel L1 adaptive control algorithm is applied to the hysteresis compensation problem of piezoelectric ceramics, thus eliminating the complicated process of hysteresis modeling in traditional methods. The piezoelectric drive system is decomposed into a hysteresis subsystem and a linear dynamic subsystem, and the output of the hysteresis subsystem is used as the input of the linear dynamic subsystem. The hysteresis is transformed into the disturbance of the linear system, and then the L1 adaptive control algorithm is used to deal with it. The stability of the system is proved by theoretical derivation. Compared with the proportional integral-differential (PID) controller in the experiment, a better control effect is obtained, and the effectiveness of the control algorithm is verified. Finally, combining the advantages of the former two methods, the L1 adaptive control algorithm based on Prandtl-Ishlinkii model is adopted. The decoupling structure is still used to describe the system, and the Prandtl-Ishlinkii model is used to transform the hysteresis. Compared with the L1 adaptive controller alone, it can not only reduce the number of uncertain parameters in the L1 adaptive controller, but also reduce the number of uncertain parameters in the L1 adaptive controller. At the same time, the range of uncertain parameters is reduced, which is beneficial to further reduce the control error.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB383.1

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