磁控形状记忆合金驱动器的强非线性动力学与控制研究

Precision actuators are one of the core components of precision machining robots. The flutters caused by joint gaps and the random disturbances in precision machining process will seriously affect the accuracy of the actuator’s action. In this proposal, a magnetic shape memory alloy self-sensing actuator is proposed to achieve the precise control of the actuator’s motion under the gap’s nonlinearity and random disturbances. Based on the hysteretic nonlinear dynamics theory and the experimental data of the magnetic shape memory alloy, a multi-field coupling hysteretic nonlinear constitutive model of the magnetic shape memory alloy is established by the normal form method and the multivariate statistical regression method. The structure of the magnetic shape memory alloy self-sensing actuator is designed, and its nonlinear dynamic model under the load is developed. The natural frequency of the strong nonlinear system is modified by the improved L-P method, and the statistic probability density function of the system’s response is obtained when the random disturbances are considered. The concept of transition sets is introduced to divide the parameter space, and the conditions of stochastic Hopf bifurcation are determined. A sliding mode control based on inverse compensation is proposed to achieve accurate and rapid system control. It can compensate the hysteresis effect of the magnetic shape memory alloy and the delay effect of the driving coils.

精密驱动器是精密加工机器人的核心部件之一。机器人关节间隙非线性引起的颤振和精密加工过程中存在的随机扰动，会严重影响驱动器动作的精度。本课题提出一种磁控形状记忆合金自传感驱动器，实现在间隙非线性和随机干扰下对驱动器动作的精准控制。基于滞后非线性动力学理论，在磁控形状记忆合金的实验数据基础上，运用规范形方法结合多元统计回归方法，建立磁控形状记忆合金的多场耦合滞后非线性本构模型；设计磁控形状记忆合金自传感驱动器，建立其在工作负载下的非线性动力学模型, 运用改进的L-P方法修正强非线性系统的固有频率；考虑随机扰动的影响，得到强非线性系统响应的稳态概率密度函数，引入转迁集思想划分系统参数空间，分析系统发生随机Hopf分岔的参数条件条件；提出一种滑模逆补偿控制，以补偿磁控形状记忆合金的滞后效应和驱动线圈的时滞效应，实现系统精确、快速控制。

手术机器人可以完成精细的手术动作, 但由于机械臂关节间隙非线性引起的颤振和人体神经、肌肉痉挛等现象产生的随机干扰会严重影响机器人动作的精准程度。本课题提出和设计了一种新型磁控形状记忆合金驱动器，实现了对机械臂在强非线性和随机干扰下的精准控制。引入非线性微分项，建立了磁控形状记忆合金材料的应力-应变连续非线性滞后模型；考虑多物理场的作用，在实验数据的基础上，运用规范形方法结合多元统计回归方法，建立了磁控形状记忆合金材料的应力-应变-磁场强度的多场耦合滞后非线性本构关系；设计并制造了磁控形状记忆合金自传感驱动器，建立了磁控形状记忆合金驱动器在简谐激励下的非线性动力学模型，提出一种适用于强非线性系统的改进L-P方法，分析了系统的强非线性动力学特性；考虑随机扰动的影响，研究了系统在随机扰动下的局部稳定性和全局稳定性，引入转迁集思想划分系统参数空间，确定了系统发生随机分岔的参数条件；通过在滑模面中引入非线性函数，提出了一种全局快速Terminal滑模控制，从而实现对磁控形状记忆合金驱动器的快速精准控制。本课题的研究成果对于推动磁控形状记忆合金驱动器的动力学特性研究，具有重要的理论意义和实际应用价值。所得结论可以为手术机器人和精密加工等精密作动提供坚实的理论支撑和应用指导。