永磁同步电动机的分数阶建模研究

发布时间：2018-05-25 18:06

本文选题：分数阶 + 建模　；参考：《华南理工大学》2014年博士论文

【摘要】：主要研究永磁同步电动机的分数阶建模，研究围绕电动机分数阶模型存在性、电动机分数阶时域建模、电动机分数阶频域建模以及基于永磁同步电动机分数阶模型的分数阶比例积分控制器的速度控制研究四个方面展开。永磁同步电动机分数阶模型的存在性是本文研究的首要问题。鉴于永磁同步电动机分数阶模型是否存在，目前尚无相关研究及其成果的报告，加之对分数阶微积分的物理机理和意义尚无统一的认识，因此很难从机理上去证明或者验证用分数阶微积分描述的电动机模型的存在。本文假设，如果分数阶模型存在，即分数阶模型比其整数阶模型更加贴近电动机的实际，那么采用依赖于模型的控制器对采用分数阶对象进行控制所得到的控制性能应该优于利用该控制器对整数阶对象进行控制的性能。本文结合仿真实验和原型实验研究的结果表明，永磁同步电动机的分数阶模型是存在的。采用机理和数据相结合的建模方法对永磁同步电动机分数阶时域建模，提出电动机的一种分数阶模型，设计伪随机激励信号，获取实时实验数据并采用数值拟合方法来获取分数阶阶次，运用分数阶系统建模中Output-error辨识算法，实现数据建模。模型验证通过原型实验，由辨识得到的永磁同步电动机分数阶模型和传统的整数阶模型采用同一控制器设计准则，在相同的实验条件下比较系统的阶跃响应跟随性能。采用机理和数据相结合的建模方法对永磁同步电动机分数阶频域建模，提出电动机的一种分数阶模型，由实时实验数据绘制出电动机的对数频率特性曲线。采用分数阶频域建模中经典Levy辨识算法，对算法在高频数据拟合好但在低频段拟合差的问题，用加权函数加以改进，得到永磁同步电动机分数阶模型辨识结果。模型验证通过原型实验，，由辨识得到的永磁同步电动机分数阶模型和传统的整数阶模型采用同一控制器设计准则，在相同的实验条件下比较系统的阶跃响应跟随性能。对永磁同步电动机时域和频域分数阶建模两种方法的过程进行了简述和比较，分数阶模型比整数阶模型对系统辨识频域数据拟合的更好。这或许可以解释电磁耦合的分布参数系统的特性不能用整数有限阶次建模，分数阶建模却可以得到更好的拟合结果。同时基于永磁同步电动机分数阶模型和整数阶模型，采用同一分数阶控制器设计准则，给出分数阶比例积分PIλ控制器的设计方法和过程，比较系统的阶跃响应跟随性能。
[Abstract]:This paper mainly studies the fractional order modeling of permanent magnet synchronous motor (PMSM), the existence of fractional-order model of PMSM, and the modeling of fractional-order time-domain of PMSM. The research on fractional order frequency domain modeling of motor and speed control of fractional order proportional integral controller based on fractional order model of permanent magnet synchronous motor (PMSM) is carried out in four aspects. The existence of fractional order model of permanent magnet synchronous motor (PMSM) is the most important problem in this paper. In view of the existence of fractional order model of permanent magnet synchronous motor, there is no report of relevant research and achievements, and there is no unified understanding of the physical mechanism and significance of fractional calculus. Therefore, it is difficult to prove or verify the existence of the motor model described by fractional calculus. This paper assumes that, if the fractional order model exists, that is, the fractional order model is closer to the actual motor than its integer order model. Then the control performance obtained by using the model-dependent controller to control the fractional order object should be better than that of using the controller to control the integer order object. The results of simulation and prototype experiments show that the fractional order model of PMSM exists. The fractional time domain model of permanent magnet synchronous motor (PMSM) is modeled by the combination of mechanism and data. A fractional order model of PMSM is proposed and the pseudo-random excitation signal is designed. The real-time experimental data are obtained and the fractional order is obtained by numerical fitting method. The Output-error identification algorithm in fractional order system modeling is used to realize the data modeling. Model verification through prototype experiments, the fractional order model and the traditional integer order model of PMSM are identified using the same controller design criterion, and the step response following performance of the system is compared under the same experimental conditions. The fractional frequency domain model of permanent magnet synchronous motor (PMSM) is modeled by the combination of mechanism and data. A fractional order model of PMSM is proposed. The logarithmic frequency characteristic curve of PMSM is drawn from the real time experimental data. The classical Levy identification algorithm in fractional frequency domain modeling is adopted. The problem that the algorithm is fitted well in high frequency data but the fitting error in low frequency band is improved by the weight function, and the result of fractional order model identification of permanent magnet synchronous motor (PMSM) is obtained. Model verification through prototype experiments, the fractional order model and the traditional integer order model of PMSM are identified using the same controller design criterion, and the step response following performance of the system is compared under the same experimental conditions. The process of fractional order modeling of permanent magnet synchronous motor in time domain and frequency domain is briefly described and compared. The fractional order model is better than the integer order model in fitting the system identification data in frequency domain. This may explain that the characteristics of electromagnetic coupled distributed parameter systems cannot be modeled with integer finite order, but fractional modeling can obtain better fitting results. At the same time, based on the fractional order model and integer order model of permanent magnet synchronous motor, the design method and process of fractional integral Pi 位 controller with the same fractional order controller are given, and the step response following performance of the system is compared.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM341

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