Fast Model Predictive Control of the Nadir Singularity in Electro-Optic Systems

Abstract

RECISION pointing and stabilization of the sightline are vital capabilities in all airborne electro-optic (EO) equipment. In traditional control theoryterminology,the pointingtask isatracking requirement,eitherofadynamictargetorsomeotherspecialpointof interest, and stabilization refers to the disturbance rejection capability of the sightline controller; typical disturbances are a combinationofownshipmotionandbearingfriction. Therelativeimportance between the pointing and stabilization tasks is a function of the intendedoperationoftheEOsystem;forexample,long-rangetargetingrequiresprecisestabilization,butanagilesightlineisessentialfor directed infrared countermeasures (DIRCM) systems [1], although both pointing and stabilization loops should be optimized for all systems. A DIRCM engagement occurs when the host platform is attacked by a surface-to-air missile, usually a shoulder-launched Man-Portable Air Defence missile, which is defeated when the DIRCM system positions a jamming signal onto the missile seeker. Obviously, accurate target tracking is essential over a full hyperhemispherical field of regard (FOR), as any tracking deficiencies are sure to be exploited by future missile guidance systems and tactics. Given the particular threat of global terrorism to the airline industry, future DIRCM systems should be small, lightweight, and costeffective for inclusion on commercial aircraft, which invariably limits the number of available axes for sightline control. A minimum of two axes are necessary to attain full hyperhemispherical FOR. The outer gimbal (OG) axis is usually constrained to rotate with respect to the platform z axis (through azimuth angle � ) and the inner gimbal (IG) with respect to the OG y axis (through elevation angle ). This is shown in Fig. 1. When the outerandinneraxesareorthogonal,thesightlinecanbepositionedto any orientation in space, as the IG and OG axes form an ideal orthogonal basis. However,whenthe innergimbal angleapproaches the nadir (defined as �� 90 deg) (i.e., the sightline becomes aligned with the axis of rotation of the outer gimbal), the pointing system experiences the loss of a degree of freedom known as gimbal