一類(lèi)采用分?jǐn)?shù)階PI~λ控制器的分?jǐn)?shù)階系統(tǒng)可鎮(zhèn)定性判定準(zhǔn)則
發(fā)布時(shí)間：2018-08-12 08:47
【摘要】：針對(duì)含有一個(gè)分?jǐn)?shù)階項(xiàng)的區(qū)間分?jǐn)?shù)階被控對(duì)象,提出了采用分?jǐn)?shù)階PI~λ控制器的閉環(huán)系統(tǒng)可鎮(zhèn)定性判定準(zhǔn)則.將閉環(huán)系統(tǒng)的特征函數(shù)分解為擾動(dòng)函數(shù)和標(biāo)稱(chēng)函數(shù),給出了擾動(dòng)函數(shù)值集頂點(diǎn)的構(gòu)造方法.根據(jù)被控對(duì)象分?jǐn)?shù)階階次和控制器的階次,研究了值集形狀是否切換和切換頻率的計(jì)算方法.此外,給出了測(cè)試頻率區(qū)間的上下界,以實(shí)現(xiàn)在有限頻率區(qū)間內(nèi)判定閉環(huán)系統(tǒng)值集與原點(diǎn)的位置關(guān)系.在假設(shè)值集頂點(diǎn)函數(shù)在測(cè)試頻率區(qū)間內(nèi)不為零和閉環(huán)標(biāo)稱(chēng)系統(tǒng)穩(wěn)定的情況下,以解析的方式提出了采用分?jǐn)?shù)階PI~λ控制器閉環(huán)系統(tǒng)的可鎮(zhèn)定性判定準(zhǔn)則.最后,通過(guò)對(duì)數(shù)值算例的可鎮(zhèn)定性分析,驗(yàn)證了提出的判定準(zhǔn)則的有效性.
[Abstract]:For an interval fractional order controlled plant with a fractional order term, a stabilization criterion for closed loop systems using fractional order PI位 controller is proposed. The eigenfunction of closed loop system is decomposed into perturbation function and nominal function. The method of constructing vertex of perturbation function value set is given. According to the fractional order of the controlled object and the order of the controller, the calculation method of whether the shape of the value set is switched and the switching frequency is studied. In addition, the upper and lower bounds of the test frequency interval are given to determine the position relationship between the value set and the origin of the closed-loop system in the finite frequency range. Under the assumption that the vertex function of the set of values is stable in the closed loop nominal system without zero sum in the test frequency range, a stabilization criterion for the closed-loop system using fractional order PI- 位 controller is proposed in an analytical manner. Finally, the validity of the proposed criterion is verified by qualitative analysis of numerical examples.
【作者單位】： 遼寧大學(xué)輕型產(chǎn)業(yè)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(61304094) 遼寧省教育廳科學(xué)研究一般項(xiàng)目(L2015194,L2015198)資助~~
【分類(lèi)號(hào)】：TP273
[Abstract]:For an interval fractional order controlled plant with a fractional order term, a stabilization criterion for closed loop systems using fractional order PI位 controller is proposed. The eigenfunction of closed loop system is decomposed into perturbation function and nominal function. The method of constructing vertex of perturbation function value set is given. According to the fractional order of the controlled object and the order of the controller, the calculation method of whether the shape of the value set is switched and the switching frequency is studied. In addition, the upper and lower bounds of the test frequency interval are given to determine the position relationship between the value set and the origin of the closed-loop system in the finite frequency range. Under the assumption that the vertex function of the set of values is stable in the closed loop nominal system without zero sum in the test frequency range, a stabilization criterion for the closed-loop system using fractional order PI- 位 controller is proposed in an analytical manner. Finally, the validity of the proposed criterion is verified by qualitative analysis of numerical examples.
【作者單位】： 遼寧大學(xué)輕型產(chǎn)業(yè)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(61304094) 遼寧省教育廳科學(xué)研究一般項(xiàng)目(L2015194,L2015198)資助~~
【分類(lèi)號(hào)】：TP273
【相似文獻(xiàn)】
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1 王振濱,曹廣益,朱新堅(jiān);一類(lèi)分?jǐn)?shù)階系統(tǒng)的辨識(shí)算法(英文)[J];Journal of Southeast University(English Edition);2004年03期
2 趙春娜;薛定宇;;一種分?jǐn)?shù)階線性系統(tǒng)求解方法[J];東北大學(xué)學(xué)報(bào)(自然科學(xué)版);2007年01期
3 朱呈祥;鄒云;;分?jǐn)?shù)階控制研究綜述[J];控制與決策;2009年02期
4 武相軍;王興元;;分?jǐn)?shù)階L，
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