An optimal explicit guidance scheme for ballistic missiles with solid motors

Due to the availability of thrust cut-off facility, the guidance problem of flight vehicles with liquid engines (atleat the last stage being a liquid engine) gets simplified to a great extent. But liquid engine propelled vehicles give rise to undesirable problems like Sloshing, Tail-Wags-Dog etc. These problems are absent in the vehicles propelled only by solid motor(s). Moreover, important factors like Instant Firing, High Reliability, Low Cost etc. are additional plus points. However the crucial point of accurate guidance is difficult in these class of vehicles, mainly due to the absence of thrust cut-off facility and also due to the unpredictibility nature of its thrust profile. In the present study, a successful guidance scheme has been developed, based on the principle of optimal control, for ballistic missiles propelled only by solid motors. Assuming the starting point of its second stage to be a deterministic point beyond atmosphere, the scheme guides the missile properly so that it intercepts the target in the prescribed error envelope, overcoming many limitations for using solid motors. Because of the classified nature and hence the associated difficulty in getting the real-life vehicle data for such class of vehicles, a two stage vehicle was designed from a preliminary staging calculation. All simulation works have been carried out based on this artificially generated, yet compatible set of data.