Preliminary pulse motor optimization for a surface-to-air missile

This paper describes the optimization of a pulse rocket motor for comparison to an existing dual-thrust motor for a surface-to-air missile. An optimization algorithm is used to select the optimal motor and guidance motor parameters so as to maximize the final velocity at intercept. The pulse motor design parameters included the fraction of the fuel in the &st pulse and the delay between the two pulses. Trajectories for an all-boost motor are also optimized for comparison purposes. The specific impulse drop of the dual-thrust motor during the sustain phase allowed the pulse-motor to achieve higher final speeds. The all-boost motor does not suffer a specific impulse drop but was outperformed by other two motors. The pulse motor combines the constant specific impulse of the allboost motor with the energy management of the dual-thrust motor to provide the best performance of the three motor types. Introduction The seminal works in the field of thrust and motor optimization used calculus ofvariations to demonstrate that the continuously-throttleable ideal boost-sustain motor maximized missile performancelva. The requirement of the use of fixed nozzle designs in actual rocket motor designs prevented these theoretical performance limits from being achieved. The practical boostsustain motor suffers a specific impulse degradation in both the boost and sustain portions of the thrust history with the greatest losses in the low bum rate sustain phase. The pulse rocket motor allows the use of nearly constant mass flow rate during operation which gives a 5-7 percent advantage in overall specific impulse over the practical boost-sustain motor. Through proper design of the motor and control algorithms, the pulsed rocket motor is able to approach the theoretical limits set for the ideal boost-sustain motor. Thus, the pulse motor should offer performance improvement over the practical boost-sustain motor. The complete solution to the optimal pulse motor problem involves simultaneous optimization of the motor parameters, ignition This paper is declared a work of the U.S. Government and is not subject to times and trajectory shaping. Two broad approaches are available for solution of this problem. The fist is the optimal control methodology which yields a two point boundary value problem. The resulting problem can be solved numerically for an open-loop solution for both the motor design and the guidance. Another method to solve the optimal control problem is to approximate the system by a reduced order model and to find the corresponding closed loop analytical guidance and ignition law. While yielding an implementable algorithm, this method involves approximations which may not be appropriate. In addition the reduced order analytical solutions do not address the selection of the pulse motor design parameters. The reduced order approach to obtain an analytical solution has been used by a number of authors. This approach has been used with success to determine pulse ignition laws to minimize time of flight and to maximize final speed during horizontal flight30'3 of an air-to-air missile. The problem of ignition of the second pulse and trajectory shaping in the vertical plane to minimize the time of flight has been addressed by reduced order approximations for an air-to-air missilee and for a surface-to-surface missile4. The use of model reduction in these solutions contributes to uncertainty as to their optimality for the complete problem. The other approach to the solution of the complete problem is parameter optimization. In this approach the optimal control is approximated by an optimal finite s e t of parameters. This method has been used to determine the range maximal motor parameters and open-loop trajectory shaping of a two pulse air-to-surface missile7. In that work the solution was subject to minimum dynamic pressure and average speed constraints for the high altitude mission and maximum altitude limit for the low-altitude mission. While the resulting open-loop trajectory shaping and pulse ignition schedule from the parameter optimization are not directly implementable in a real time system, such an approach remains a valuable tool. During the copyright protection in the United States