Energy management for multiple-pulse missiles

This paper examines maximum final speed and minimum flight-time trajectories of missiles that have two- or three-pulse rockets for both horizontal and vertical plane flight. The optimal rocket-propellant loadouts and pulse ignition times are determined using parameter optimization coupled with explicit solution of the trajecto- ries. The results indicate that the three-pulse configuration is superior for both problems in horizontal flight and that it matches the performance of an ideal boost-sustain motor. For vertical plane flight, the twb:0ulse motor is superior to a boost-only motor. The three-pulse motor does not produce a significant practical improvement in performance for vertical plane flight beyond that of the two-pulse motor. HE development of practical designs for pulsed solid rocket motors has opened new avenues for the control of missile trajectories. To effectively utilize this new technology, techniques must be developed to optimize the trajectories and pulse motor designs. The present paper seeks to create a method to rapidly optimize pulse rocket-motor designs and trajectories and to determine the applicability of pulse motors to a spectrum of missile missions with an emphasis on the surface-to-air missile. The seminal works in the field of rocket-thrust and rocket - motor design optimization used the calculus of variations to demonstrate that the continuously throttleable ideal boost- sustain motor maximized missile performance.1'2 The require- ment of the use of fixed nozzle designs in actual rocket-motor designs prevented these theoretical performance limits from being achieved. The practical boost-sustain motor suffers a specific impulse degradation in both the boost and sustain portions of the thrust history with the greatest losses in the low-burn-rate sustain phase. The pulse rocket motor allows the use of nearly constant mass flow rate during operation, which gives a 5-1% 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 perfor- mance improvement over the practical boost-sustain motpr. The complete solution to the optimal pulse motor problem involves simultaneous optimization of the motor parameters, ignition times, and trajectory shaping. Two broad approaches are available for solution of this problem. The first is the optimal control methodology, which yields a two-point boundary value problem. The resulting problem can be solved numerically using an open-loop solution for both the motor design and the missile 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 approxima- tions which may not be appropriate. In addition, the reduced- order analytical solutions do not address the selection of the pulse motor design parameters.