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Optimal Missile Guidance system

Optimal Missile Guidance system. By Yaron Eshet & Alon Shtakan Supervised by Dr. Mark Mulin. Equations of motion. Target. Missile. Interception - Overview. Parameters : Interception:. Necessary condition for interception for all initial conditions :

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Optimal Missile Guidance system

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  1. Optimal Missile Guidance system By Yaron Eshet & Alon Shtakan Supervised by Dr. Mark Mulin

  2. Equations of motion Target Missile

  3. Interception - Overview Parameters: Interception: Necessary condition for interception for all initial conditions: The problem: non-linear and complex relation between the parameters • The solution: • Guidance law in (RTPN) to achieve • b) Guidance law in to complete the interception process

  4. Test case Simple maneuver simulates realistic missile

  5. Test case – Guidance law RTPN: Realistic true proportional navigation Guidance law perpendicular to line of sight (LOS(: compensation of target missile acceleration

  6. Test case – Guidance law distance decrease: has a projection in direction Target LOS Missile

  7. Test Case: equations of motion Initial conditions

  8. Interception in 37.57 sec

  9. Interception time vs.  • The influence of  depends on the initial conditions  difference in interception time of order 0.1 sec  difference in interception time of order 10 sec

  10. Interception time vs.  • For  values under a certain bound, there is no guarantee for interception Interception time diverges for small values of 

  11. Interception time vs.  • Saturation zone: minor influence of . Critical influence for initial conditions and maneuver interception time ~ 37 sec interception time ~ 200 sec

  12. Analytical analysis Necessary condition for interception for all initial conditions (1) resulting condition (2)

  13. Behavior of with respect to  (comparison with theory) =3.85 (interception) =1.51 (interception) =1.49 (interception) =0.9 (miss) Edge of divergence extreme divergence divergence occurs around r0 , as  starts varying rapidly

  14. ? ensures interception for all initial conditions depends on maneuver The solution: guidance law also in direction

  15. ?

  16. Summery: sufficient conditions for interception K>0 1.5< These conditions ensure interception for all initial conditions and for any target missile maneuver.

  17. Gain Scheduling - K The case: delay in data acquisition about the target missile maneuver  limited sensitivity sec 203.73 212.08

  18. Gain Scheduling -  The case: adjusting for distance increase/decrease not negligible  sec 47.34 49.68

  19. Constraints on interception time: Optimal control

  20. Example: Limited angular acceleration

  21. No limit No interception

  22. Transition from failure to successful interception (green plot – previous page) Conclusion: Under realistic constraints, one gets an upper bound for K, which means a lower bound for interception time

  23. Ideal interception vs. interception under constraint (blue vs. red plots) No constraint Conclusion: Interception with no constraint is faster indeed. However, it requires homing missile with higher performance and greater control effort.

  24. Project summery • Analysis of the equations of motion of the system • Introduction of guidance laws and study of their function in ensuring interception • Applying “Gain Scheduling” methods for improved performance • Analysis of the system behavior under realistic constraints and restrictions

  25. The End

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