
Theterminal guidancedesign problem fora long-rangebank-to-turn (BTT)ramjetmissileinvolvesa completely coupled pitch ‐yaw‐roll nonlinear dynamics model. Because of these nonlinear dynamics, an optimal solution for acceleration and roll-rate commands can be found only by numerical methods for solving two-point boundary value problems. Because the roll-rate dynamics of the state-of-the-art missiles is much faster than the rest of the systemstates,anear-optimalsolutionisobtainedtotheBTTguidanceproblemusing multipletimescaletechniques. Nonlinear feedback solutions for the acceleration command and roll-rate command are derived. The zero-order slow solution obtained by treating roll rate as ine nitely fast, is exactly the optimal guidance law for a skid-to-turn missile.Thezero-orderfastsolutionprovidestheroll-ratecommand.Ae rst-orderanalysiscorrectstheacceleration command for the e nite dynamics behavior in bank angle. Simulation results are presented for a representative terminal engagement using this algorithm. Near-zero miss distances are obtained in a noise-free environment.
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