The problem of minimum-time attitude control of a spinning missile is addressed. The missile is modeled as a rigid body which is symmetric about one axis. The missile is assumed to have a large roll rate about this axis of symmetry. Control is achieved by a single reaction jet which, when fired, provides a constant moment about a transverse axis. Disturbance torques are assumed to be zero. The equations of motion are written under these assumptions. The missile is assumed to have some arbitrary initial transverse angular velocity and it is desired to take it to some final attitude in minimum time while reducing the transverse angular velocity to zero. This problem is formulated as an optimal control problem. Instead of taking the conventional approach of solving a two point boundary value problem, we consider an alternative approach. This approach deals with the specific case where only two thruster firings are sufficient to change the attitude of the missile in minimum time. By iterating on the switch times and integrating the state equations, we can compute the thruster firing times for a given set of boundary conditions. Some examples are included to illustrate the application of the concepts presented. We conclude by proposing a mechanization of this control scheme and pointing out some further research directions.

The problem of minimum-time attitude control of a spinning missile is addressed. The missile is modeled as a rigid body that is symmetric about its spin axis. A single reaction jet provides the necessary transverse moments. The missile is assumed to have some arbitrary initial transverse angular velocity, and it is desired to take it to some final attitude in minimum time while reducing the transverse angular velocity to zero. A scheme to generate thruster firing times as functions of the initial and desired states of a spinning missile is described. This scheme involves transforming the state variables and integrating the transformed state and costate equations backward in time and generating the control history using the properties of the optimal control. The control history, given in terms of the thruster firing times, is stored as a function of the boundary conditions. A feedback control law based on function generation is then proposed that uses only the first thruster turn-on and turn-off times. This proposed control scheme can be implemented in real time with good accuracy.

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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.