發(fā)布時(shí)間：2018-10-23 21:27

【摘要】：分?jǐn)?shù)階系統(tǒng)是整數(shù)階系統(tǒng)的一般化,因?yàn)槠潆A數(shù)可以為任意實(shí)數(shù),在描述動(dòng)態(tài)系統(tǒng)上具有更大的靈活性。此外,分?jǐn)?shù)階控制器相比于整數(shù)階控制器具有階數(shù)可調(diào)的新優(yōu)勢(shì)。因此,分?jǐn)?shù)階系統(tǒng)分析及分?jǐn)?shù)階控制方法已成為研究熱點(diǎn)。然而,分?jǐn)?shù)階微分是非局部算子,相比于整數(shù)階微分其計(jì)算要復(fù)雜得多。為此,本文運(yùn)用分?jǐn)?shù)階積分運(yùn)算矩陣開展了分?jǐn)?shù)階系統(tǒng)分析、分?jǐn)?shù)階系統(tǒng)辨識(shí)等相關(guān)問題的研究。主要工作如下:考慮到分?jǐn)?shù)階微分的非局部性特征,運(yùn)用Haar小波來(lái)逼近系統(tǒng)的輸入、輸出信號(hào),給出一種基于Haar小波積分運(yùn)算矩陣的分?jǐn)?shù)階系統(tǒng)分析方法,推導(dǎo)了分析過程,并通過系統(tǒng)準(zhǔn)確解和其它算法結(jié)果的對(duì)比驗(yàn)證了所提方法的正確性。分?jǐn)?shù)階系統(tǒng)辨識(shí)相比整數(shù)階系統(tǒng)辨識(shí)要復(fù)雜,主要是系統(tǒng)階數(shù)辨識(shí)的問題,若把分?jǐn)?shù)階階數(shù)當(dāng)成參數(shù)直接辨識(shí)會(huì)導(dǎo)致一個(gè)非線性優(yōu)化問題,為此,本文通過給定階數(shù)將其轉(zhuǎn)化為最小二乘優(yōu)化問題,然后采用在一定范圍內(nèi)尋找最優(yōu)階數(shù)的辦法來(lái)避免非線性優(yōu)化問題。除此之外,受小波多分辨分析的啟發(fā),通過舍棄輸入輸出的高頻系數(shù)來(lái)降低運(yùn)算矩陣維數(shù),最終,給出了一種能夠加快分?jǐn)?shù)階系統(tǒng)辨識(shí)的方法。通過對(duì)已知系統(tǒng)的辨識(shí)驗(yàn)證了方法的可行性和正確性,并將所提方法應(yīng)用到多質(zhì)量彈性扭轉(zhuǎn)系統(tǒng)辨識(shí)上,通過整數(shù)階模型辨識(shí)和分?jǐn)?shù)階模型辨識(shí)的比較,結(jié)果表明分?jǐn)?shù)階模型的均方誤差更小。根據(jù)辨識(shí)的多質(zhì)量彈性扭轉(zhuǎn)系統(tǒng)模型,設(shè)計(jì)了PIλD)μ控制器對(duì)系統(tǒng)進(jìn)行控制,仿真結(jié)果表明,分?jǐn)?shù)階IλDμ較整數(shù)階PID控制器具有更好地控制效果,分?jǐn)?shù)階PIλD μ控制效果在實(shí)際平臺(tái)上得到了驗(yàn)證。
[Abstract]:Fractional order system is the generalization of integer order system, because its order can be arbitrary real number, so it has more flexibility in describing dynamic system. In addition, fractional order controller has a new advantage over integer order controller. Therefore, fractional order system analysis and fractional order control methods have become a hot topic. However, fractional differential is more complicated than integer differential. Therefore, in this paper, fractional order system analysis and fractional order system identification are studied by using fractional integral operation matrix. The main work is as follows: considering the nonlocal characteristic of fractional differential, using Haar wavelet to approximate the input and output signals of the system, a method of fractional order system analysis based on Haar wavelet integral matrix is presented, and the analysis process is deduced. The correctness of the proposed method is verified by comparing the system exact solution with the results of other algorithms. Fractional order system identification is more complicated than integer order system identification, which is mainly the problem of system order identification. If fractional order system is directly identified as a parameter, it will lead to a nonlinear optimization problem. In this paper, the given order is transformed into the least square optimization problem, and then the method of finding the optimal order in a certain range is used to avoid the nonlinear optimization problem. In addition, inspired by the wavelet multi-resolution analysis, the dimension of the operation matrix is reduced by abandoning the high-frequency coefficients of the input and output. Finally, a method to speed up the fractional system identification is presented. The feasibility and correctness of the proposed method are verified by the identification of known systems, and the proposed method is applied to the identification of multi-mass elastic torsion systems. The comparison between integer order model identification and fractional order model identification is given. The results show that the mean square error of fractional order model is smaller. According to the identified multi-mass elastic torsion system model, the PI 位 D) 渭 controller is designed to control the system. The simulation results show that the fractional order I 位 D 渭 has better control effect than the integer order PID controller. The fractional-order PI 位 D 渭 control effect is verified on a practical platform.
【學(xué)位授予單位】：南京信息工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：N945.14;O231

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本文編號(hào)：2290510