A scheme to generate thruster firing times for the time-optimal reorientation of a spinning missile

Abstract

A sclicinc to generate tlrruster firing tiincs as functions of tlic initial and the desired state of a spinning iriissil~ is dcscribcd. The missile is niodelcd as arigid body w l i i c l i is syminctric about one axis and which Iias a large roll rabc about this axis of symmetry. Coiitrol is achieved by a single reaction jet which, w l i c i i fired, pro\,idcs a constant inorricr~t abont a traiisvcrsc axis. 1ht.iirbaiice torqncs are assumed to tic x r o . 'l'lic missile is assumed to have some arhit.rary initial transvcrsc angnlar velocity and it is d c s i w d to take it to sonic final attitude in minimum timc wliilc rcdncing t,lic transverse angular velocity 0 . This inininittni-time reorientation probleni ally hniidlcrl by solving a TPDVP ( T w o I'cint Jhrindary Valuc Problcni). Tlic control liistory thus otjt,iiiiicd is stored i n an oil-board computer plcnrriit.ed oii-line by table look-lip. \ \ ' e d scliiviic wliicli docs not nccd to solve a TI'DVI'. 111s t i x d , coordin;rt.e t.ransforiiiations arc iiscd siicli that cacli Ijackwards int,egratioii of the traiisfornicd s t a k a n d costate equations yields a unique time-optiinal trajcct,ory. Ry storiiig the st,at,c and tlic associated t,iine-optiinal control at discrete points i n timc, a sct of bornidary condition points can be generated for wliicli (,lie niinimnni-tiinc control is known. This set of poiiit,s can later be uscd to gciierat,c a table of l , l~r i~s t o r firing t i m r s as functions of tlic ctirrcnt and t,lic drsircd stzitc of tlic missile. Sonic crainplcs are plot lid t,o illiist.rat,e thr applicat.ion of t,lic concepts prrwiI1 cd.

Multiple-input describing function technique applied to design a single channel ON-OFF controller for a spinning flight vehicle

“…An ON-OFF actuator is usually simpler than a proportional actuator but it increases the non-linearity of the flight control system. ON-OFF actuators have been used for time-optimal attitude control of spacecraft [19][20][21][22][23] and spinning missiles [24,25]. Lateral pulse jets have also been proposed for the lateral control of spinning rockets and missiles [26,27].…”