Ph.D Student Sigal Erez Sub-Optimal Solution to a Non-Linear Missile Guidance Problem Department of Aerospace Engineering Professor Yoseph Ben-Asher Abstract

A study of planar non-linear missile guidance is presented. The model is characterized by a) Non linear geometry with large deviations from a collision course, b) Aerodynamic forces depending on velocity and angle of attack, c) Thrust generated by a rocket motor resulting in changes in velocity and mass, and d) Missile flight is controlled using the angle of attack and rocket motor ignition timing.

Previous studies on missile guidance focused on two main disciplines. Terminal guidance laws aim at minimizing miss distances. They are usually developed under linearization assumptions and result in closed form analytic laws. Mid-course guidance emphasis is on energy conservation, resulting in elevated trajectories. Usually, the solutions are numerical and involve approximations.

The first goal of this study is developing a guidance law for between mid-course and terminal homing phases. This kind of law is based on complex models to capture the non linear nature of the flight, but simple enough to result in analytic solutions.

A resent development in solid rocket motor technology is the multiple pulse motor. It allows ignition of predefined pulses on demand according to guidance system commands.

The second goal of this study is expanding the previous work on utilizing pulse motor technology in missile guidance. This study gives a unified guidance and pulse motor ignition time scheme.

With the above goals in mind, this work studies a horizontal planar non linear scenario.

Five different sub problems are solved, they are differentiated by the propulsion method.

The solution method that was developed, includes a combination of three methods: treating the system equations as a switched system, optimal control, and the singular perturbations method. This solution method results in a simple to implement analytic solution to the problems.

During the problem solution, a new condition in the minimum principle was derived. The condition pertains to switched systems with system equations dependent on the switching time.

An augmented rocket motor equation was developed. This equation expands the classic rocket equation to include the effect of drag under several assumptions: constant altitude, constant thrust and constant drag coefficient.

The guidance law developed couples the pulse ignition command and the guidance command for the first time.

A reference solution is calculated using the collocation method. The collocation method was expanded for use in switched systems. Comparison shows the new guidance scheme is indeed near optimal.