MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (II)

IntroductionThecorrespondencebetweenH∞ decentralizedcontrolandmodalsynthesistheoryispresentedinpart (I)ofthepaper[1].WheretheorthogonalityandtheexpansiontheoremofeigenfunctionsofsubsystemsH∞ controlareintroduced .Basedontheseresults,thefollowingsectionspresentthemodalsynthesismethodforthecomputationoftheoptimalH∞ normofthedecentralizedcontrolsystemsandnumericalexamples.Notethatthroughoutthepaperequation(I_n)denotesequation (n)inpart (I)ofthepaper[1].1　OptimalParameterComputationforGlob…     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H∞ DECENTRALIZED CONTROL SYSTEMS （II）

When using H∞ techniques to design decentralized controllers for large systems, the whole system is divided into subsystems, which are analysed using H∞ control theorybefore being recombined. An analogy was established with substructural analysis instructural mechanics, in which H∞ decentralized control theory corresponds to substructuralmodal synthesis theory so that the optimal H∞ norm of the whole system corresponds to thefundamental vibration frequency of the whole structure. Hence, modal synthesismethodology and the extended Wittrick-Williams algorithm were transplanted from structuralmechanics to compute the optimal H∞ norm of the control system. The orthogonality and theexpansion theorem of eigenfunctions of the subsystems H~ control are presented in part (I)of the paper. The modal synthesis method for computation of the optimal H∞ norm ofdecentralized control systems and numerical examples are presented in part (Ⅱ).     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H∞ DECENTRALIZED CONTROL SYSTEMS （ I ）

When using H∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H∞ control theorybefore being recombined. An analogy was established with substructural analysis instructural mechanics, in which H∞ decentralized control theory corresponds to substructuralmodal synthesis theory so that the optimal H∞ norm of the whole system corresponds to thefundamental vibration frequency of the whole structure. Hence, modal synthesismethodology and the extended Wittrick-Williams algorithm were transplanted from structuralmechanics to compute the optimal H∞ norm of the control system. The orthogonality and theexpansion theorem of eigenfunctions of the subsystems H∞ control are presented in part(I) of the paper. The modal synthesis method for computation of the optimal H∞ norm ofdecentralized control systems and numerical examples are presented in part (Ⅱ).     

VARIATIONAL METHOD AND COMPUTATION FOR H_∞ CONTROL

ＩｎｔｒｏｄｕｃｔｉｏｎＨ∞ｃｏｎｔｒｏｌｔｈｅｏｒｙｈａｓｂｅｅｎｗｅｌｌｄｅｖｅｌｏｐｅｄｓｉｎｃｅｔｈｅＤＧＫＦｐａｐｅｒ[1],ｗｈｅｒｅｔｈｅｆｕｎｄａｍｅｎｔａｌｅｑｕａｔｉｏｎｓｆｏｒＨ∞ ｍｅａｓｕｒｅｍｅｎｔｆｅｅｄｂａｃｋｃｏｎｔｒｏｌａｒｅｄｅｒｉｖｅｄｆｒｏｍｔｈｅｓｅｐａｒａｔｉｏｎｐｒｉｎｃｉｐｌｅ ,ａｓｉｎＬＱＧｃｏｎｔｒｏｌｔｈｅｏｒｙ[2～ 5 ].Ｈｏｗｅｖｅｒ,ｔｈｅｃｏｍｐｕｔａｔｉｏｎｆｏｒｆｉｎｉｔｅｈｏｒｉｚｏｎ [0 ,ｔｆ]ｐｒｏｂｌｅｍａｎｄｔｈｅｄｅｔｅｒｍｉ…