本文選題：分?jǐn)?shù)階微積分　切入點(diǎn)：超穩(wěn)定性理論　出處：《南京理工大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：模型參考自適應(yīng)控制器(Model Reference Adaptive Controller,MRAC)在工程實際中應(yīng)用廣泛,為獲得更加優(yōu)異的性能而對其控制策略進(jìn)行分?jǐn)?shù)階延伸,具有一定的理論和實際意義。針對目前分?jǐn)?shù)階MRAC設(shè)計方法中存在的穩(wěn)定性問題,以及控制策略選取復(fù)雜和適用范圍局限的現(xiàn)狀,本文基于Popov超穩(wěn)定性理論給出了分?jǐn)?shù)階MRAC的設(shè)計方法,并通過非線性前饋/狀態(tài)反饋(Nonlinear Feedforward/State Feedback,FF/FB)變換將其適用對象推廣到一類非線性系統(tǒng)。同時,將所得成果應(yīng)用到質(zhì)子交換膜燃料電池(Proton Exchange Membrane Fuel Cell,PEMFC)的熱管理系統(tǒng)中。本文的主要內(nèi)容有:1.基于Popov超穩(wěn)定性理論以及分?jǐn)?shù)階微積分的定義和性質(zhì),證明了在改變分?jǐn)?shù)階MRAC控制律積分階次時,控制系統(tǒng)仍能滿足超穩(wěn)定性定理,且類比于整數(shù)階控制器常用的基于狀態(tài)變量和輸入-輸出兩類設(shè)計方法,給出了分?jǐn)?shù)階MRAC的具體設(shè)計過程。2.基于微分幾何理論,利用相對階概念對干擾進(jìn)行分類,提出了具有可測干擾的MIMO非線性系統(tǒng)的線性化方法—非線性前饋/狀態(tài)反饋(Nonlinear Feedforward/State Feedback,FF/FB)變換,將控制器的適用對象成功拓展到一類非線性系統(tǒng)。3.以5kW水冷型PEMFC發(fā)電系統(tǒng)為研究對象,建立了 PEMFC熱管理系統(tǒng)的溫度模型,通過FF/FB變換,有效實現(xiàn)了溫度模型的線性化;同時,為滿足溫度控制對精度和魯棒性的要求,設(shè)計了分?jǐn)?shù)階MRAC,該控制器改善了控制系統(tǒng)的動態(tài)性能,提高了其抗干擾能力。
[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.
【學(xué)位授予單位】：南京理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TM911.4;TP273

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