基于超稳定理论的分数阶模型参考自适应控制器设计与应用

发布时间：2018-03-19 04:27

本文选题：分数阶微积分　切入点：超稳定性理论　出处：《南京理工大学》2017年硕士论文　论文类型：学位论文

【摘要】：模型参考自适应控制器(Model Reference Adaptive Controller,MRAC)在工程实际中应用广泛,为获得更加优异的性能而对其控制策略进行分数阶延伸,具有一定的理论和实际意义。针对目前分数阶MRAC设计方法中存在的稳定性问题,以及控制策略选取复杂和适用范围局限的现状,本文基于Popov超稳定性理论给出了分数阶MRAC的设计方法,并通过非线性前馈/状态反馈(Nonlinear Feedforward/State Feedback,FF/FB)变换将其适用对象推广到一类非线性系统。同时,将所得成果应用到质子交换膜燃料电池(Proton Exchange Membrane Fuel Cell,PEMFC)的热管理系统中。本文的主要内容有:1.基于Popov超稳定性理论以及分数阶微积分的定义和性质,证明了在改变分数阶MRAC控制律积分阶次时,控制系统仍能满足超稳定性定理,且类比于整数阶控制器常用的基于状态变量和输入-输出两类设计方法,给出了分数阶MRAC的具体设计过程。2.基于微分几何理论,利用相对阶概念对干扰进行分类,提出了具有可测干扰的MIMO非线性系统的线性化方法—非线性前馈/状态反馈(Nonlinear Feedforward/State Feedback,FF/FB)变换,将控制器的适用对象成功拓展到一类非线性系统。3.以5kW水冷型PEMFC发电系统为研究对象,建立了 PEMFC热管理系统的温度模型,通过FF/FB变换,有效实现了温度模型的线性化;同时,为满足温度控制对精度和鲁棒性的要求,设计了分数阶MRAC,该控制器改善了控制系统的动态性能,提高了其抗干扰能力。
[Abstract]:Model Reference Adaptive Controller (MRAC) is widely used in engineering practice. In order to obtain better performance, its control strategy is extended in fractional order. It has some theoretical and practical significance. Aiming at the stability problems existing in fractional order MRAC design method, and the current situation of complex control strategy selection and limited application range, Based on the theory of Popov hyperstability, the design method of fractional order MRAC is given in this paper. The nonlinear Feedforward/State feedback / nonlinear feedback FF / FB transformation is applied to a class of nonlinear systems. The results obtained are applied to the thermal management system of proton Exchange Membrane Fuel PEMFC.The main contents of this paper are: 1. Based on the Popov hyperstability theory and the definition and properties of fractional calculus, It is proved that when the integral order of fractional MRAC control law is changed, the control system can still satisfy the hyperstability theorem, and it is analogous to two kinds of design methods based on state variables and input-output for integer order controllers. The design process of fractional order MRAC is given. 2. Based on the theory of differential geometry, the concept of relative order is used to classify interference. In this paper, a linearization method for MIMO nonlinear systems with measurable disturbances is presented, which is called nonlinear feedforward / state feedback nonlinear Feedforward/State feedback FF- / FBtransform. The suitable object of the controller is successfully extended to a class of nonlinear systems .3.Taking 5kW water-cooled PEMFC power generation system as the research object, the nonlinear feedforward / state feedback nonlinear feedforward / state feedback nonlinear feedforward / state feedback nonlinear Feedforward/State feedback nonlinear system is proposed. The temperature model of PEMFC thermal management system is established, and the linearization of the temperature model is realized through FF/FB transformation, and in order to meet the requirement of precision and robustness of temperature control, Fractional order MRAC is designed. The controller improves the dynamic performance of the control system and improves its anti-jamming ability.
【学位授予单位】：南京理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TM911.4;TP273

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