智能逆系统理论及其在感应电机解耦控制中的应用
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摘要
非线性系统控制在控制科学中占有重要的地位。20世纪80年代以来,逆系统控制在非线性控制领域得到蓬勃发展。它通过引入α-阶积分逆和伪线性系统等概念,建立起比较完整的设计理论。但该方法要求被控对象的数学模型精确已知,而这在实际工程应用中是难以实现的。尤其是针对一些复杂系统,很难求出其解析逆系统。这都成为了逆系统的实际应用的“瓶颈”。
本文主要利用神经网络、支持向量机等智能机器学习方法不依赖精确数学模型的特点,结合逆系统理论,给出了智能逆系统控制方法和一些重要的结论。
首先,在广义逆系统控制中,控制器必须与复合伪线性系统的传递函数相互配合才能使整个控制系统达到满意的动态控制效果。传统广义逆系统控制系统在改变复合系统期望传递函数时,必须重新辨识广义逆系统。本文提出了一种新的广义逆系统,并证明了该广义逆系统的存在性。改变反馈系统的参数即可任意配置复合伪线性系统的极点,通过调节控制器参数和广义逆系统的反馈环节参数即可改善整个控制系统的动态性能,并应用于感应电机解耦控制中,获得良好的控制效果。
为提高逆系统的鲁棒性,结合区间分析理论,在传统自组织映射的基础上,提出了权值为区间数的区间自组织模型和相应的学习算法,分别对区间权值的上、下界进行训练,并证明了该算法的收敛性。结合VQTAM方法对动态信息的存储能力,建立非线性系统的逆模型,增强了控制系统处理不确定性的能力。
针对良好非线性模型及其线性化补偿器问题,证明两者在一定约束条件下存在的惟一性。在此基础上,提出一种利用神经网络优化新的目标函数而得到辨识模型的新方法。为提高系统鲁棒性,减小模型误差和外部扰动等不确定性,针对补偿后的伪线性系统设计非线性内模控制系统,使得整个控制系统能精确的跟踪参考信号。
逆系统控制的关键在于构建的逆系统模型的推广能力。本文给出一种基于最小二乘支持向量机在线算法的α-阶逆控制方法。通过引入系统控制误差的ε不敏感函数,利用LS-SVM增量-枝剪学习算法,对逆系统控制器实施在线学习,增强了伪线性复合系统的精确性和鲁棒性。并在LS-SVM的核函数为局部Lipschitz的前提下,证明了控制器是有限增益稳定的,并给出Gaussian核函数对任一变量的局部Lipschitz性的充分条件。
最后,在感应电机矢量控制基础上,对其进行逆系统控制解耦性能、抗扰动性能和鲁棒性方面的仿真实验,证实了新型广义逆系统控制的有效性。针对利用单一神经网络难以实现感应电机大范围内的线性化解耦问题,结合多模型理论和新型广义逆系统,给出了感应电机神经网络多模型广义逆系统解耦控制方法。通过建立多个子广义逆系统、设计与子系统匹配的控制器和制定适当的定切换规则,实现了感应电机转速和磁链在大范围内的动态解耦控制。
Nonlinear system control plays an important role in the control science. Inverse system control gets flourish development in nonlinear control since 1980s.It has established perfect design theory by introducing some definitions such asα-th order inverse, pseudo linear system and so on. But the exact mathematical model is required in the inverse system control and the model is hardly satisfied in engineering. It is hard to get the analytical inverse, especially to some complicated systems. These are the bottlenecks in the inverse system theory.
Combining with intelligent machine learning methods, as neural networks and support vector machines which are independent on mathematical model, intelligent inverse system control method and some significant results are proposed in this thesis.
Firstly, the whole control system can exhibit satisfactory dynamic result only by perfect matching the controller and composite pseudo linear system in the generalized inverse control. The traditional generalized inverse must be re-identified with the variation of the expected transfer function. A new type of generalized inverse system is proposed here and its existence is proved. The poles of the pseudo linear system can be assigned via altering the parameters of the feedback part arbitrarily. The dynamic performance of the control system can be improved by regulating the parameters of controller and feedback part. By using this method, induction motor decoupling control can obtain good results.
To improve the robustness of inverse, interval self-organizing maps and its learning algorithm is proposed based on interval analysis theory and traditional self-organizing map. The upper and lower boundaries of interval weights are trained and the convergence of the map is proved by combining the capability of VQTAM in storing the information of dynamic system, the nonlinear inverse model is built to deal with uncertainty.
The uniqueness of the nicely nonlinear model and its linearizing compensator is proved under some constraints. A new model identification method is proposed by minimizing a novel objective function using neural networks. A nonlinear internal control system is designed on the compensated pseudo-linear system to improve the robustness and reduce the uncertainty including model error and external disturbance. The whole control system can track the reference signal accurately.
The key of inverse control is the generalization of the inverse system. An a th-order inverse control method based on least square support vector machines(LS-SVM) on-line algorithm is presented. The inverse execute online learning with incremental and decremental algorithm by introducingεinsensitive function which enhances the accuracy and robustness of the pseudo linear system. The finite gain stability is ensured if the kernel function of LS-SVM is local Lipschitz, and the sufficient condition of local Lipschitz of Gaussian kernel function to any variable is given.
At last, the validity of new type of generalized inverse control is proved via simulations of decoupling performance, disturbance-rejection performance and robustness based on vector control. While it is hard to achieve decoupling control on induction motor in a wide range using single neural networks. A multi-model decoupling method is proposed using multi-model theory and the new type of generalized inverse. The rotor flux and rotor speed of induction motor can be decoupled in a wide range by constructing several sub-generalized inverse, designing relevant controller and formulating proper switching rules.
本文主要利用神经网络、支持向量机等智能机器学习方法不依赖精确数学模型的特点,结合逆系统理论,给出了智能逆系统控制方法和一些重要的结论。
首先,在广义逆系统控制中,控制器必须与复合伪线性系统的传递函数相互配合才能使整个控制系统达到满意的动态控制效果。传统广义逆系统控制系统在改变复合系统期望传递函数时,必须重新辨识广义逆系统。本文提出了一种新的广义逆系统,并证明了该广义逆系统的存在性。改变反馈系统的参数即可任意配置复合伪线性系统的极点,通过调节控制器参数和广义逆系统的反馈环节参数即可改善整个控制系统的动态性能,并应用于感应电机解耦控制中,获得良好的控制效果。
为提高逆系统的鲁棒性,结合区间分析理论,在传统自组织映射的基础上,提出了权值为区间数的区间自组织模型和相应的学习算法,分别对区间权值的上、下界进行训练,并证明了该算法的收敛性。结合VQTAM方法对动态信息的存储能力,建立非线性系统的逆模型,增强了控制系统处理不确定性的能力。
针对良好非线性模型及其线性化补偿器问题,证明两者在一定约束条件下存在的惟一性。在此基础上,提出一种利用神经网络优化新的目标函数而得到辨识模型的新方法。为提高系统鲁棒性,减小模型误差和外部扰动等不确定性,针对补偿后的伪线性系统设计非线性内模控制系统,使得整个控制系统能精确的跟踪参考信号。
逆系统控制的关键在于构建的逆系统模型的推广能力。本文给出一种基于最小二乘支持向量机在线算法的α-阶逆控制方法。通过引入系统控制误差的ε不敏感函数,利用LS-SVM增量-枝剪学习算法,对逆系统控制器实施在线学习,增强了伪线性复合系统的精确性和鲁棒性。并在LS-SVM的核函数为局部Lipschitz的前提下,证明了控制器是有限增益稳定的,并给出Gaussian核函数对任一变量的局部Lipschitz性的充分条件。
最后,在感应电机矢量控制基础上,对其进行逆系统控制解耦性能、抗扰动性能和鲁棒性方面的仿真实验,证实了新型广义逆系统控制的有效性。针对利用单一神经网络难以实现感应电机大范围内的线性化解耦问题,结合多模型理论和新型广义逆系统,给出了感应电机神经网络多模型广义逆系统解耦控制方法。通过建立多个子广义逆系统、设计与子系统匹配的控制器和制定适当的定切换规则,实现了感应电机转速和磁链在大范围内的动态解耦控制。
Nonlinear system control plays an important role in the control science. Inverse system control gets flourish development in nonlinear control since 1980s.It has established perfect design theory by introducing some definitions such asα-th order inverse, pseudo linear system and so on. But the exact mathematical model is required in the inverse system control and the model is hardly satisfied in engineering. It is hard to get the analytical inverse, especially to some complicated systems. These are the bottlenecks in the inverse system theory.
Combining with intelligent machine learning methods, as neural networks and support vector machines which are independent on mathematical model, intelligent inverse system control method and some significant results are proposed in this thesis.
Firstly, the whole control system can exhibit satisfactory dynamic result only by perfect matching the controller and composite pseudo linear system in the generalized inverse control. The traditional generalized inverse must be re-identified with the variation of the expected transfer function. A new type of generalized inverse system is proposed here and its existence is proved. The poles of the pseudo linear system can be assigned via altering the parameters of the feedback part arbitrarily. The dynamic performance of the control system can be improved by regulating the parameters of controller and feedback part. By using this method, induction motor decoupling control can obtain good results.
To improve the robustness of inverse, interval self-organizing maps and its learning algorithm is proposed based on interval analysis theory and traditional self-organizing map. The upper and lower boundaries of interval weights are trained and the convergence of the map is proved by combining the capability of VQTAM in storing the information of dynamic system, the nonlinear inverse model is built to deal with uncertainty.
The uniqueness of the nicely nonlinear model and its linearizing compensator is proved under some constraints. A new model identification method is proposed by minimizing a novel objective function using neural networks. A nonlinear internal control system is designed on the compensated pseudo-linear system to improve the robustness and reduce the uncertainty including model error and external disturbance. The whole control system can track the reference signal accurately.
The key of inverse control is the generalization of the inverse system. An a th-order inverse control method based on least square support vector machines(LS-SVM) on-line algorithm is presented. The inverse execute online learning with incremental and decremental algorithm by introducingεinsensitive function which enhances the accuracy and robustness of the pseudo linear system. The finite gain stability is ensured if the kernel function of LS-SVM is local Lipschitz, and the sufficient condition of local Lipschitz of Gaussian kernel function to any variable is given.
At last, the validity of new type of generalized inverse control is proved via simulations of decoupling performance, disturbance-rejection performance and robustness based on vector control. While it is hard to achieve decoupling control on induction motor in a wide range using single neural networks. A multi-model decoupling method is proposed using multi-model theory and the new type of generalized inverse. The rotor flux and rotor speed of induction motor can be decoupled in a wide range by constructing several sub-generalized inverse, designing relevant controller and formulating proper switching rules.
引文
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