分数阶微积分算子的逼近方法及其应用

发布时间：2018-03-01 21:27

本文关键词： ??IDP 控制器有理函数逼近离散化分抗元件向量法增强鲁棒　出处：《长春理工大学》2016年硕士论文　论文类型：学位论文

【摘要】：分数阶微积分是一种广义的微积分,其阶次不仅覆盖整数,还包括小数部分,乃至复数。有理逼近方法、数值计算方法、集成电路及计算机技术等的迅速发展极大地促进了分数阶微积分理论的深入研究,并逐渐渗透到其它的重要应用领域。在控制领域中,由于某些被控对象存在不同程度的非整数阶特性,同时大量的研究表明,分数阶控制器具有不同于整数阶控制器的控制性能,因而分数阶微积分领域产生了一大批追随者。分数阶系统建模与辨识、运算电路、控制器设计与实现及滤波器等在控制领域中都有重要的应用。分数阶微积分算子的逼近方法与数值实现是分数阶系统控制问题的研究前提。因此,本论文首先研究了该算子的z域离散化方法以及s域逼近方法,然后在复频域函数逼近理论的基础之上,构造该算子的近似函数,提出在s域中,近似误差以及逼近区间可调实用的分数阶微积分算子的近似方法。本文还给出了其相关物理器件、电路,主要包括分抗元件的实现和分数阶微积分电路的实现;从现有方案存在的缺陷入手,提出了新的电路设计,即采用基于s域连乘积式的有理函数逼近方法来设计分抗元件和分数阶微积分器。并且以s域连乘积式的有理函数逼近方法为基础,对分数阶微积分算子间接离散化,从而完成了??IDP控制器的数字实现。在整个??IDP控制器设计中,还需要求解其参数,本文给出了两种整定策略,第一种策略为基于向量的Flat Fhase控制器参数简化整定,第二种策略为增强型的鲁棒??IDP参数整定。仿真结果表明,所提出的分数阶微积分算子的逼近算法是有效的,基于此两种方法设计出来的??IDP控制器具有很好的控制性能。本文的创新点是:给出了分数阶微积分算子的有理逼近算法,并将此方法应用到其微积分电路的设计上,同时也将此算法移植到数字??IDP控制器的设计上,并给出了两种新的参数整定方法:基于向量法的??IDP控制器参数简化整定方法以及增强鲁棒??IDP参数整定方法。
[Abstract]:Fractional calculus is a kind of generalized calculus. Its order not only covers integers, but also includes fractional part, complex number, rational approximation method and numerical method. The rapid development of integrated circuits and computer technology has greatly promoted the in-depth study of fractional calculus theory, and gradually penetrated into other important application fields. Because of the non-integer order characteristics of some controlled objects, a lot of researches show that the fractional order controller is different from the integer order controller in its control performance. As a result, a large number of followers have emerged in the field of fractional calculus. The design and implementation of controller and filter have important applications in the field of control. The approximation method and numerical realization of fractional calculus operator are the premise of the control problem of fractional system. In this paper, the discretization of the operator in z domain and the approximation method in s domain are studied. Then, based on the theory of function approximation in complex frequency domain, the approximate function of the operator is constructed and proposed in the s domain. The approximate error and the approximate method of approximate interval adjustable fractional calculus operator are given. The related physical devices and circuits are also given in this paper, including the realization of fractional reactance element and fractional calculus circuit. Starting with the defects of the existing schemes, a new circuit design is proposed. The rational function approximation method based on the continuous product in s domain is used to design the fractional reactance element and fractional calculus, and based on the rational function approximation method of the continuous product in s domain, the fractional calculus operator is indirectly discretized. And it's done? ? Digital implementation of IDP controller. ? In the design of IDP controller, it is necessary to solve its parameters. In this paper, two tuning strategies are given. The first strategy is to simplify the parameter tuning of Flat Fhase controller based on vector, and the second is to enhance the robustness of the controller. ? IDP parameter tuning. Simulation results show that the proposed fractional calculus operator approximation algorithm is effective, based on these two methods designed? ? IDP controller has good control performance. The innovation of this paper is: the rational approximation algorithm of fractional calculus operator is given, and this method is applied to the design of its calculus circuit, at the same time, the algorithm is transplanted to digital? ? In the design of IDP controller, two new parameter tuning methods are given: based on vector method? ? IDP controller parameter simplified tuning method and enhanced robustness? ? IDP parameter tuning method.
【学位授予单位】：长春理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O174.41

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