Empirical Virtual Sliding Target Guidance law

1. Empirical Virtual Sliding Target Guidance law Presented by: Jonathan Hexner Itay Kroul Supervisor: Dr. Mark Moulin

2. Introduction • A new guidance law for long range surface to air missiles is tested. • Guidance law is empirical based on aerodynamic considerations. • Idea: missile achieves a high altitude during boost phase, allowing low drag during pursuit of target. • Altitude is achieved using a virtual sliding target (VST), initialized at a high altitude sliding towards target. • Basic guidance scheme used to guide the missile towards VST and real target is proportional navigation (PN).

3. 2D Missile Engagement model • Legend: • T – Thrust • m – missile mass • g – gravity • D – Drag q - Line of site (LOS) angle am - missile flight path angle at - target flight path angle • ac - commanded acceleration perpendicular to LOS • am - missile acceleration perpendicular to missile body. • vm - missile velocity. • vt - target velocity. • at - target acceleration • Equations of motion

4. Augmented Proportional Navigation • APN is the optimal guidance law for a non inertial system in the sense that is minimal • APN navigation: • Substituting into the guidance law:

5. VST Guidance law - detailed • Stage 1: Missile guidance towards VST: • Boost Phase: missile guided towards stationary point. • Midcourse Phase: missile guided towards virtual target, which slides towards target. Guidance cycle: • tgo estimated: • Predicted Intercept Point (PIP) of missile and target is calculated: • VST slides towards PIP. Sliding velocity: • Missile guided towards new VST location.

6. VST Guidance Law – Cont’d • Stage 2: Missile guidance towards target: • Missile guided towards target at lock-on range from target.

7. Simulation model • Missile Specifications: • Thrust model: • Atmospheric conditions: • Propellant mass rate of change:

8. Simulation Model – cont’d • Drag: • Angle of attack ≤ 30° CD0 profile: CD0 - zero lift dragcoefficient CDi - induced drag coefficient y T x S - wetted surface area. D mg

9. Non maneuvering target example

10. VST testing • VST compared with PN in several nominal scenarios: • Approaching & Receding Non maneuvering target. • Approaching & Receding maneuvering target (at>0, at<0). • Different VST0 tested. • Parameters tested: • Interception time • Velocity at lock on – correlates with launch boundary envelope • Missile initial conditions constant: • vm0 = 100 [m/sec] • am0 = 10° y x

11. Simulation (1)– Non Maneuvering Receding target Target parameters: VST0

12. Simulation (2) – Non Maneuvering Approaching target Target parameters: VST0

13. Simulation (3) – Maneuvering Receding Target Target parameters: VST0

14. Simulation (4) – Maneuvering Approaching Target Target parameters: VST0

15. Simulation (5) – Maneuvering Receding Target Target parameters: VST0

16. Simulation (6) – Maneuvering Approaching Target Target parameters: VST0

17. Non Linear sliding velocity • Non linear: • Initially faster slide: vinlf = vilFeft F>0,f<0 • Initially slower slide: vinls = vilS(est -1) S>0,s>0 • Initially faster => lower altitude • Initially slower => higher altitude • Very unstable • Recall: Approaching target example (VST0 = [1km,15km])

18. Summarizing results • Unsuccessful choice of VST0: • Low missile velocity at lock on • Missile misses target • Successful choice of VST0: • High missile velocity at lock on (increased launch boundary)

19. Summary & Conclusions • VST guidance law was tested using various target scenarios with different VST0 positions. • Results show similar behavior for maneuvering and non-maneuvering targets: • Increased velocity at lock-on for approaching target. • Increased intercept time. • Main advantage: simple implementation. • Drawbacks: lacks analytic basis, not robust to VST0 position.

20. Questions???