Stiffness matrix correction from incomplete test data

A survey on moving mass control technology

In some smart weapons, estimation of the impact point of the shell at each computation cycle of the control law is an integral part of the control strategy. In these situations, the impact point predictor is part of the imbedded computing system onboard the projectile. Practical considerations dictate that the impact point predictor yield rapid yet reasonably accurate estimates. Common methods for rapid trajectory prediction are numerical integration of point mass dynamic equations and evaluation of approximate closed-form solutions of the rigid-body projectile dynamic equations. These methods are shown to exhibit poor impact point prediction for long-range shots with high gun elevations characteristic of smart indirect fire munitions. Through modifications of projectile linear theory, a rapid projectile impact point predictor is proposed that eliminates the accuracy problems of the other methods while preserving low computational requirements. Typical results are provided for a short-range trajectory of a direct fire fin-stabilized projectile and a long-range trajectory for an indirect fire spin-stabilized round to substantiate these claims.

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Modified Projectile Linear Theory for Rapid Trajectory Prediction

Uncontrolled direct fire atmospheric rockets exhibit high impact point dispersion, even at relatively short range, and, as such, have been employed as area weapons on the battlefield To reduce the dispersion of a direct fire rocket, the use of a small number of short-duration lateral pulses acting as a control mechanism is investigated A unique control law is reported that combines model predictive control and linear projectile theory for lateral pulse jet control of an atmospheric rocket The impact point in the target plane is directly controlled Through simulation, this model predictive flight control law is shown to efficiently reduce direct fire rocket dispersion A parametric trade study on an example rocket configuration is reported that details the effect of the number and amplitude of individual pulse jets, as well as the effect of the flight control system computation cycle time

Model Predictive Lateral Pulse Jet Control of an Atmospheric Rocket

_ / Magnus moment \ V */2PSlVpd / = axial and transverse moments of inertia = amplitudes of the two yaw model arms for a symmetric missile = trim angle magnification factor = reference length = mass -XYZ components of the missile's angular velocity = reference area = dynamic stability factor = 2c0/d0o gyroscopic stability factor = (op) /4C^ = time = magnitude of the missile velocity = missile-fixed axes, the X axis along the longitudinal axis of the missile, positive forward = nonspinning aeroballistic axes = angles of attack and sideslip in the missilefixed system = circular limit motion radius = polar angle of £ = K j / K j ( j = l , 2 ) = value of \j for a linear Magnus moment = the complex angle of attack in the missile-fixed system = 0 4ict = be i9

Symmetric Missile Dynamic Instabilities

The stability of a spinning projectile which contains a cylindrical mass fitted loosely into a cylindrical cavity but constrained to spin with the projectile is examined. An unstable coning motion is obtained in which spin decay and cone angle growth are proportional to the coefficient of friction between the mass and the cavity wall and to the maximum angle of cant between the mass and the projectile. Similar behavior is observed experimentally.

William G. Soper

Papers

Projectile instability produced by internal friction