永磁同步电机分数阶混沌动力学行为分析与控制研究

A permanent magnet synchronous motor (PMSM) is a kind of high-efficient and high-powered motors. Permanent magnet synchronous motors (PMSM) will demonstrate complexity chaotic phenomena when its parameters fall into a certain area. Chaotic phenomena has been the important factors leading the performance of PMSM degrade and instability. This project intends to construct the model of PMSM fractional-order chaotic system by employing fractional derivatives at first. Then, based on the air-gap PMSM fractional order chaotic model, the dynamical behaviors such as horseshoe topology structure dimension and phase space fractal characteristics have been investigated in detail. Meanwhile, the improved time-domain predictor-corrector algorithm and frequency domain recursive algorithm have been given. Based on these two algorithms, the fractional-order chaotic of motor in frequency domain has been optimized under fitting approximation error analysis. Through the optimization, the higher precision has been obtained than the traditional numerical algorithm. Furthermore, according to a designed novel mesh topological alterable order analog fractance circuit, a coupling fractional chaotic oscillation circuit has been constructed in order to coupled the fractional-order chaotic behaviors of PMSM. Furthermore, a three-channel circuit has been given by using the mesh fractance unit for hardware implementation the fractional-order coupled chaotic circuit and to demonstration the fractional behaviors in simulation results of fractional-order chaotic attractors of PMSM. Finally, the fractional-order proportional control strategy based on the fractional projective function has been illustrated to achieve coupling synchronization of fractional-order chaotic trajectory of PMSM system. In a word, this research not only solves the control problem of fractional-order chaotic phenomena in permanent magnet synchronous motor, but also using the designed fractional-order chaotic circuit for hardware implementation of the PMSM chaotic attractors in non-integer order form.

永磁同步电机混沌振荡一直是电机运行失稳的重要因素，电机混沌行为的分数阶表征及其动力学相关研究至今尚未展开。 本项目拟基于分数阶微积分算子理论构造永磁同步电机分数阶混沌动力学数学模型，研究气隙均匀状态下分数阶混沌吸引子的马蹄拓扑结构、合维数以及相空间分维特征等动力学特性。提出改进的时域预估-校正算法及频域滤波递归算法，通过算法对电机分数阶混沌频域欠拟合进行近似误差分析，通过算法寻优获得比传统数值算法更高的拟合精度。提出可变阶网型分抗单元，基于该电路单元设计永磁同步电机分数阶耦合混沌振荡电路，搭建硬件电路验证电机分数阶混沌振荡的动态相轨迹及吸引子特征。提出基于比例函数的分数阶投影控制策略，设计有效的控制器使分数阶吸引子达到耦合同步。 本课题的研究不仅解决了永磁同步电机分数阶混沌行为的建模与同步控制问题，而且所设计的分数阶耦合混沌电路为研究电机系统混沌行为开辟了新的路径。

永磁同步电机（PMSM）被广泛的应用于航空航天、电动汽车、机器人等高新技术领域，实际运行中的永磁同步电机系统伪随机非线性振荡时有发生，尤其是系统参数落入某些区域后产生的分岔及混沌振荡一直是电机系统运行失稳的重要因素。然而永磁同步电机混沌振荡行为的分数阶表征及其动力学研究尚未完全展开。本项目考虑电机运行中振荡的分数维特征，采用分数阶微积分算子理论构造了永磁同步电机分数阶动力学模型，研究气隙均匀状态下分数阶混沌吸引子的马蹄拓扑结构、合维数以及相空间分维特征等动力学特性。提出改进的时域预估-校正算法及频域滤波递归算法，通过算法对电机分数阶混沌频域欠拟合进行近似误差分析，通过算法寻优获得比传统数值算法更高的拟合精度。提出可变阶网型分抗单元，基于该电路单元设计永磁同步电机分数阶耦合混沌振荡电路，搭建硬件电路验证电机分数阶混沌振荡的动态相轨迹及吸引子特征。提出基于比例函数的分数阶投影控制策略，设计有效的控制器使分数阶吸引子达到耦合同步。 提出非终端结构的滑模变结构控制策略对永磁同步电机的混沌行为进行有效控制及干预，并将改进型滑模控制器应用于永磁同步电机无位置传感器的控制中。 本课题的研究不仅可以解决永磁同步电机分数阶混沌行为的建模与同步控制问题，而且所设计的分数阶耦合混沌电路为研究电机系统混沌行为开辟了新的路径。