m: IodepeDdent &YhJ slpam C b n M (lnw is a ant& SabQe that dccwplu tbe space structure into n independent sccmd-opder sutuystarr u m r d i n g to I) crntrolled modes md cmtmlsescdrpdellldegreadeo tly. I t is d-l h r o r m Uut the l?E r l t e s cmtml and atemation spillover caused wben tbe amaeatiaaal crypled mdal m t r o l scbm? i s employed. rlx independent cmtml of each d e requires tbat the number of .cfwtars k ah is this paper, ~ ~ p r q x s e a amM scheme that U o w s one to ust? a reduced number of actuators to control a l l modelled modes d c ~ t i m a l l ~. J ~ I particular, the method of generalized in-matrims is en(played to iplement tbe actuetars sud, tbat ule u ' m p a l u e r of the d c s e d-l q system are ar dared as parsihIe to those specified ly the cptimal MFC. Chquter siraulatim of t h e m mntml-Q) a s h q ~ l y-t e d k is giioen. 1. IllIRoousRM me develcpmt of the space shuttle has the poesibility of constructing very large structures i n space for space aplaratiom. amtrol pmblens for Lss are attitude antrol and sbape rmtrol. cclpplex missions impose many stringent requiremu an shape a d attitude of the Lss, which lead the a n t r o l researchers to the cnrept of distributed active amtrol w!we severdl actuatas ard sasors are placed an the structure to in ader to optimize its performaace ard beharior. %e has been a mmiderable interest in the area of active control of large space structures (US) [11-[131. A number of control sdxmes were stubied, but they represent cne form r n-mother of rodal control t61. d n d a l control schemes are the carpled Ddal antrol Md the Wependent lbdal Space Ccntrol (ItW). '& fmmx uses an active codroller that ansists of a state c s t i m t a and a state feedback; the latter deoxplea tbe 1ss into n ixlepenQnt subsystems aomrdmg to n antrolled .odes md cmtmls ed.l PDde iaQpaden t l y by means of a aodal filter 1 5 I a d an optimal antroller. CaJpled Ip3dal control c a w omtrol .ad abservrrtian spillover that tollether can destabilize the Lss 1101. Msc does not have the spillover prcblap since each d e is cantrolled independently. trowever in order to-1-t the Msc the nmber of actuators is required to be hrse far a faithful Ddelling of the us. mis fact p-esents a h-damental linitatim of M S C since the required number of r h r a h is d i z a b l e. l b e main objective of this paper is to h l e D e n t the Msc with a milder requirement of the actuator nuber. In other words. we w i l l develop a m t r o l sdwne tbat uses a reduaed MIlrber of actuatcrs to antml a l l mo&elled in such a way that the pdes of the closed-locp systm are as closed as possible to the optimal mdes spxified by tbe I)6c rcheae. In particular, the method of generalized inverre matrices is-1-f t x the hlenentatiar of Msc. equal to tbe armber of m 1 e d EuIks, Rly hi& far d faithful .odeL2q Of 1-dpaCV StnrCtwPS. fi equal to the rnmrber of amtrolled modes whidl is usually very Watrix notaticns used in this paper is given. belaw: ~~ {NASA-CR-182336) O P T I H A L CONTROL OE' // 9 2 2 s-i;' g 0 ... 0 ...
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