典型文献
Multiplicity-induced optimal gains of an inverted pendulum system under a delayed proportional-derivative-acceleration feedback
文献摘要：
This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration(PDA)feedback,which can be used to understand human balance in quiet standing.The closed-loop system is described by a neutral delay differential equation(NDDE).The optimal feedback gains(OFGs)that make the exponential decaying rate maximized are determined when the characteristic equation of the closed-loop has a repeated real root with multiplicity 4.Such a property is called multiplicity-induced dominancy of time-delay systems,and has been discussed intensively by many authors for retarded delay differential equations(RDDEs).This paper shows that multiplicity-induced dominancy can be achieved in NDDEs.In addition,the OFGs are delay-dependent,and decrease sharply to small numbers correspondingly as the delay increases from zero and varies slowly with respect to moderate delays.Thus,the inverted pendulum can be well-stabilized with moderate delays and relatively small feedback gains.The result might be understandable that the elderly with obvious response delays can be well-stabilized with a delayed PDA feedback controller.
文献关键词：
中图分类号：
作者姓名：
Zisong MEI;Zaihua WANG
作者机构：
Department of Basic Courses,Army Engineering University,Nanjing 211101,China
文献出处：
引用格式：
[1]Zisong MEI;Zaihua WANG-.Multiplicity-induced optimal gains of an inverted pendulum system under a delayed proportional-derivative-acceleration feedback)[J].应用数学和力学（英文版）,2022(11):1747-1762
A类：
NDDE,OFGs,dominancy,RDDEs,NDDEs,understandable
B类：
Multiplicity,induced,optimal,gains,inverted,pendulum,delayed,proportional,derivative,acceleration,feedback,This,paper,studies,stabilization,PDA,which,can,used,human,balance,quiet,standing,closed,loop,described,by,neutral,differential,that,make,exponential,decaying,maximized,are,determined,when,characteristic,has,repeated,real,root,multiplicity,Such,property,called,systems,been,discussed,intensively,many,authors,retarded,equations,shows,achieved,In,addition,dependent,decrease,sharply,small,numbers,correspondingly,increases,from,zero,varies,slowly,respect,moderate,delays,Thus,well,stabilized,relatively,result,might,elderly,obvious,response,controller
AB值：
0.475748
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