Trajectory optimization using indirect methods and parametric scramjet cycle analysis

Joseph Williams, Purdue University


This study investigates the solution of time sensitive regional strike trajectories for hypersonic missiles. This minimum time trajectory is suspected to be best performed by scramjet powered hypersonic missiles which creates strong coupled interaction between the flight dynamics and the performance of the engine. Comprehensive engine models are necessary to gain better insight into scramjet propulsion. Separately, robust and comprehensive trajectory analysis provides references for vehicles to fly along. However, additional observation and understanding is obtained by integrating the propulsion model inside the trajectory framework. Going beyond curve fitted thrusting models, an integrated scramjet cycle analysis offers rapid trade studies on engine parameters and enables the identification of the most significant and optimal engine parameters for the mission as a whole. Regularization of bang-bang control problems by use of the Epsilon-Trig regularization method has created the possibility to preserve the original equations of motion while still solving these problems through indirect methods. Indirect methods incorporate mathematical information from the optimal control problem to provide high quality, integrated solutions. The minimum time optimal trajectory of a rocket propelled missile is compared to that of a scramjet powered missile to determine the advantages of scramjet technology in this application.




Grant, Purdue University.

Subject Area

Aerospace engineering

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