本文關(guān)鍵詞： 分?jǐn)?shù)階微積分 分?jǐn)?shù)階PI~γ、PI~γD~μ控制器 敏感傳遞函數(shù) 穩(wěn)定域 參數(shù)整定 液位控制　出處：《天津科技大學(xué)》2015年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：過(guò)去我們用整數(shù)階微積分方程描述自然界中的事物,但隨著科學(xué)技術(shù)的發(fā)展,我們發(fā)現(xiàn),自然界中許多現(xiàn)象依靠傳統(tǒng)整數(shù)階微分方程式是不能精確描述的。其實(shí),現(xiàn)實(shí)的世界本質(zhì)上大部分都是分?jǐn)?shù)階的。所以,分?jǐn)?shù)階模型理所應(yīng)當(dāng)就成為描述自然界現(xiàn)象的數(shù)學(xué)模型。分?jǐn)?shù)階微積分對(duì)于我們所能看到的、所能感受到的、所能控制的自然世界中的事物具有很大的影響。本文首先介紹分?jǐn)?shù)階微積分理論的發(fā)展及背景,然后,以THJSK-1型水箱綜合實(shí)驗(yàn)平臺(tái)為實(shí)驗(yàn)背景,研究水箱綜合控制系統(tǒng)、水箱模型的建立、時(shí)滯系統(tǒng)及其特點(diǎn)以及分?jǐn)?shù)階算子的近似,并在此基礎(chǔ)之上,利用可應(yīng)用于分?jǐn)?shù)階系統(tǒng)的敏感傳函的界與系統(tǒng)幅值裕度和相角裕度的關(guān)系,研究了滯后系統(tǒng)的PIλ、PIλDμ控制器的參數(shù)穩(wěn)定域和參數(shù)整定方法,給出了滿足要求的控制器參數(shù)的完整區(qū)域。本文做了以下工作：(1)根據(jù)水箱實(shí)驗(yàn)設(shè)備及工作原理,通過(guò)水箱液位控制實(shí)驗(yàn)建立了單容水箱的數(shù)學(xué)模型,并驗(yàn)證了模型的正確性與有效性。(2)針對(duì)建立的時(shí)滯系統(tǒng),應(yīng)用敏感傳函的界與系統(tǒng)幅值裕度和相角裕度的關(guān)系,研究其分?jǐn)?shù)階PIλ、PIλDμ控制器的參數(shù)整定。并與傳統(tǒng)的控制器參數(shù)下的控制效果相比較,通過(guò)MATLAB仿真驗(yàn)證了分?jǐn)?shù)階控制器能夠獲得比整數(shù)階更好的動(dòng)態(tài)性能。本文的主要?jiǎng)?chuàng)新點(diǎn)是利用敏感傳函的界與系統(tǒng)的幅值裕度和相角裕度直接相關(guān),給出了系統(tǒng)相對(duì)穩(wěn)定性的信息。采用一種代數(shù)方法,在控制器的參數(shù)穩(wěn)定域內(nèi),按敏感傳函的界進(jìn)行PIλ、PIλDμ控制器的參數(shù)整定。具體的仿真實(shí)例和水箱實(shí)驗(yàn)證明了該方法設(shè)計(jì)的PIλ控制器具有良好的動(dòng)態(tài)性能和魯棒性,驗(yàn)證了該方法的有效性。
[Abstract]:In the past, we used to describe things in nature with integral order calculus, but with the development of science and technology, we found that many phenomena in nature can not be accurately described by traditional integer order differential equations. The real world is essentially fractional. So fractional order models are, of course, mathematical models that describe natural phenomena. Fractional calculus is what we can see and feel. This paper first introduces the development and background of fractional calculus theory, and then, taking the THJSK-1 water tank synthesis experimental platform as the experimental background, studies the water tank integrated control system. The establishment of the water tank model, the characteristics of the time-delay system and the approximation of fractional order operators. On the basis of this, the relationship between the bounds of sensitive transmissions applicable to fractional order systems and the amplitude margin and phase margin of the system is used. In this paper, the parameter stability region and parameter tuning method of Pi 位 N Pi 位 D 渭 controller for hysteretic systems are studied, and the complete region of controller parameters satisfying the requirements is given. The following work is done: 1) according to the experimental equipment and working principle of water tank, The mathematical model of a single tank is established through the water tank level control experiment, and the correctness and validity of the model are verified. For the time-delay system established, the relation between the bounds of the sensitive function and the amplitude margin and the phase angle margin of the system is applied. The parameter tuning of the fractional Pi 位 PI-位 D 渭 controller is studied, and the control effect is compared with that of the traditional controller. The MATLAB simulation shows that the fractional order controller can achieve better dynamic performance than the integer order. The main innovation of this paper is that the bounds of the sensitive function are directly related to the amplitude margin and the phase angle margin of the system. The information of the relative stability of the system is given. An algebraic method is used in the parameter stability domain of the controller. The parameter tuning of Pi 位 PI-位 D 渭 controller is carried out according to the bounds of sensitive transmissions. The simulation examples and water tank experiments show that the Pi 位 controller designed by this method has good dynamic performance and robustness, and the effectiveness of the proposed method is verified.
【學(xué)位授予單位】：天津科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：TP273

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