一类具有应力相关迟滞非线性智能结构的建模与跟踪控制研究

智能结构在变化的负载下产生的应力相关迟滞非线性严重影响了其在亚微米级跟踪控制中的应用. 因此, 本文提出了一种应力相关Preisach算子用以描述当输入信号与应力同时变化时, 智能结构所产生的迟滞非线性特性. 该应力相关Preisach算子是在经典Preisach算子的基础上, 通过将应力相关项引入密度函数所得到的. 此外, 为了实现逆补偿控制器的设计, 本文提出了应力相关Preisach算子的性质与基于模糊树方法的辨识方案. 继而, 本文设计了一种基于所提算子的前馈逆补偿与反馈控制器结合的复合控制方案, 并将其应用于一类超磁致伸缩智能结构的实时跟踪控制实验中. 实验证明, 与经典Preisach算子相比, 所提出的算子和相应的控制方案能够较好的消除应力相关迟滞非线性的影响并使控制效果显著提高.

On Modeling and Tracking Control for a Smart Structure with Stress-dependent Hysteresis Nonlinearity

The performance of smart structures in trajectory tracking under sub-micron level is hindered by the stress-dependent hysteresis generated by varying mechanical loads. In this paper, a stress-dependent Preisach operator is proposed for describing the hysteresis nonlinearity under both varying input current and compressive stress featured by introducing the dependence of the density function on the compressive stress. Subsequently, the properties together with the parameter identification scheme based on a fuzzy tree method of the presented operator are investigated to formulate an inverse compensator. Then, a feedback control scheme combined with a feed-forward compensator is implemented to a magnetostrictive smart structure (MSS) for real-time precise trajectory tracking. Compared with the classical operator, the proposed operator and corresponding control scheme experimentally demonstrate a dramatically improved performance for mitigating the effects of stress-dependent hysteresis.