结构振动系统鲁棒稳定控制器的参数化设计
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摘要
基于特征结构配置方法,讨论了一类匹配的结构振动系统的鲁棒控制问题,目的是设计鲁棒稳定控制器使得不确定闭环系统的特征值始终位于复平面的左半平面中某扇形区域内。给出了所期望的鲁棒稳定控制器存在的充分条件及其参数化形式,该控制器中的自由参数向量为控制系统设计提供了很大的自由度,可适当选择来满足设计中的其它性能指标。给出的数值例子说明了鲁棒稳定控制器的参数化设计方法的有效性。
Based on eigenstructure assignment,the problem of robust stabilizing controllers for a class of uncertain structural vibration systems satisfying matching conditions is investigated.Its aim is to design some controllers that can make the closed-loop eigenvalues of the system still lie in some sector area included in the left half plane of the complex planes.Then the existence condition and the parametric expressions for the gain matrices are given.The free parameter vectors in the solutions offer more freedom degrees,which can be further utilized to satisfy certain performance specifications in some system designs.Finally,a numerical example shows the effect of the parametric approach.
Based on eigenstructure assignment,the problem of robust stabilizing controllers for a class of uncertain structural vibration systems satisfying matching conditions is investigated.Its aim is to design some controllers that can make the closed-loop eigenvalues of the system still lie in some sector area included in the left half plane of the complex planes.Then the existence condition and the parametric expressions for the gain matrices are given.The free parameter vectors in the solutions offer more freedom degrees,which can be further utilized to satisfy certain performance specifications in some system designs.Finally,a numerical example shows the effect of the parametric approach.
引文
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[2]Schm itendorfW E.D es ign M ethodo logy for R obustS tab iliz ing Con tro llers[J].A u tom atica,1992,27(2):1059-1060.
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[4]Duan G R.So lu tions of the Equation AV+BW=CFand T he ir A pp lication to E igenstructure A ss ignm en tin L inear System s[J].IEEE T ransactions on A u to-m atic Con tro l,1993,38(2):276-280.
[5]Duan G R,Patton R J.E igenstructure A ss ignm en tin D escriptor System s V ia S tate F eedback:A N ewCom p lete Param etric A pproach[J].In t.J.SystemSc ience,1998,29(2):167-178.
[6]Duan G R,L iu G P.Com p lete Param etric A pproachfor E igenstructure A ss ignm en t in A C lass of Sec-ond-O rder L inear System s[J].A u tom atica,2002,38(4):725-729.
[7]Duan G R,W ang G S,L G P.E igenstructure A s-s ignm en t in A C lass of Second-O rder L inear Sys-tem s:A Com p lete Param etric A pproach[C].P ro-ceed ings of the CACSSUK,M anchester,UK,2002,89-96.
[8]Duan G R,W ang G S.E igenstructure A ss ignm en t inA C lass of Second-O rder D escriptor L inear Sys-tem s:A Com p lete Param etric A pproach[J].In ter-nationa l Journa l of A u tom ation and Com pu ting,2005,2(1):1-5.
[9]W ang G S,Duan G R.R obust Po le A ss ignm en t V iaP-D F eedback in A C lass of Second-O rder D ynam icSystem s[C].In ternationa l Con ference of A u tom a-tion,R obots and Com pu ter V is ion,K unm ing,Ch i-na,2004.
[10]W ang G S,L iang B,Duan G R.R econ figuring Sec-ond-O rder D ynam ic System s V ia S tate F eedbackE igenstructure A ss ignm en t[J].In ternationa l Jour-na l of Con tro l,A u tom ation,and System s,2005,3(1):109-116.
[11]W ang G S,Lv Q,Duan G R.D es ign of R econ figur-ing Con tro l System s v ia S tate F eedback E igenstruc-ture A ss ignm en t[J].In ternationa l Journa l of In for-m ation T echno logy,2005,11(7):61-70.
[12]段广仁,王国胜.矩阵方程EV J2+AV J+CV=BW的两种解析通解[J].哈尔滨工业大学学报,2005,37(1):1-4.
[13]王国胜,吕强,梁冰,段广仁.不确定二阶动力学系统的鲁棒特征结构配置设计[J].系统工程与电子技术,2006,28(2):271-274.
[14]王国胜,张春巍,段广仁,欧进萍.基于特征结构配置算法的结构鲁棒控制及仿真[J].地震工程与工程振动,2005,25(2):125-129.
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