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Research Papers

Adjoint Analysis of Guided Projectile Terminal Phase

[+] Author and Article Information
Timo Sailaranta

 Aalto University School of Engineering, P. O. Box 14400 FI-00076 Aalto, Finlandtimo.sailaranta@tkk.fi

Ari Siltavuori

 Aalto University School of Engineering, P. O. Box 14400 FI-00076 Aalto, Finland

J. Appl. Mech 78(5), 051009 (Aug 05, 2011) (6 pages) doi:10.1115/1.4004277 History: Received November 25, 2010; Revised March 04, 2011; Published August 05, 2011; Online August 05, 2011

Guided projectile terminal phase against target at ground level is investigated using an adjoint simulation. A pseudo-optimal projectile navigation gain is looked for against a target disturbing the projectile guidance. The use of counter-measures is “modeled” as a suddenly detected target abrupt motion during the guidance terminal phase. The miss distances obtained are studied and the projectile optimal navigation gain is chosen based on the maximum tolerated miss distance.

Copyright © 2011 by American Society of Mechanical Engineers
Topics: Projectiles
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References

Figures

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Figure 1

A generic canard-controlled guided projectile

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Figure 2

Autopilot block diagram. The gain values solved are G1  = 1.1494, G2  = 0.0221, G3  = 7.1408, and G4  = −0.0781 (Ma = 0.9 at flight altitude 1000 m).

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Figure 3

Projectile response to 5 g lateral acceleration command (Ma = 0.9 at flight altitude 1000 m). The equivalent time constant τ (63% of command reached) without seeker-head contributions is about 0.25 s.

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Figure 4

Angle of attack time history

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Figure 5

Fin deflection histories obtained

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Figure 6

The time-forward missile guidance loop used in this study. The adjoint model is based on this original system.

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Figure 7

The end game geometry studied. The projectile approaches about from above and the target is located at the origin at ground level 0 m. The true target abrupt motion is detected at some point of the terminal phase. In the adjoint simulations the sudden movement will take place at all tgo values (all distances) in one run.

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Figure 8

The target end game maneuvers as a result of velocity oscillation for 0−10 s motion. The projectile is approaching the coordinate system Origin from about above. The target motion from the origin is detected during the terminal phase.

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Figure 9

The miss distances in case of a pure target lateral velocity as a function of the flight time or time-to-go

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Figure 10

The miss distances in case of target constant lateral velocity and cosine distributed longitudinal velocity. The results are presented as a function of the time-to-go and the adjoint and nonlinear results are compared (N = 3). About 10 time-forward runs were carried out to obtain the comparison data.

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Figure 11

The miss distances in case of target constant lateral velocity and sinusoidal longitudinal velocity as a function of the time-to-go. The results are presented as a function of the time-to-go and the adjoint and nonlinear results are compared (N = 3).

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Figure 12

The miss distances in case of target constant lateral velocity and cosine distributed longitudinal velocity. The results are presented as a function of the time-to-go. The adjoint and nonlinear results also with g-limit effects included are compared (N = 3).

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Figure 13

The miss distances obtained for the N = 1 case. The gain is too small to make the projectile maneuver enough to hit the target.

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Figure 14

The miss distances obtained for the N = 2 case

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Figure 15

The miss distances obtained for the N = 3 case. The gain gives most hit opportunities.

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Figure 16

The miss distances obtained for the N = 4 case

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