A unified approach to vehicle design, control, and flight path optimization

Abstract

A set of vehicle design and control optimization methods is presented that minimizes the difference between the desired and actual dynamical flight paths. The approach taken seeks the optimum, physically admissible mass properties and/or the thrust history of the vehicle to minimize a quadratic measure of departure from the desired path. The minimization process developed here belongs to a family of problems which are commonly referred to as constrained parameter optimization. A recursive quadratic programming algorithm is used to implement the analytical formulation as a numerical algorithm. The first section of the dissertation provides the derivations of the equations of motion for fixed and variable mass bodies which include the unification of the control volume and particle dynamics analyses of the variable mass body problem. In the second section, analytical and numerical optimization procedures are discussed in detail. Suboptimal control is employed to parameterize the functional optimal control problem and thereby convert it into a constrained parameter optimization problem. This conversion process creates a unified solution methodology for the parameter optimization approach for solving this family of optimal control problems. The third section defines basic concepts and measures of stability and robustness of "motion-matching" in terms of the uniform boundedness of the deviation from the desired flight path. The analytical stability analysis of the optimized body produces "similarity parameters" for perfect motion-matching. Finally, the theoretical results are illustrated with a set of test cases (axisymmetric, sphere-cone reentry body). The fixed mass cases provide the dominant similarity parameters, whereas the variable mass bodies determine the effects of the mass-flow-induced terms, an isentropic nozzle, and a tandem optimization technique. The fixed mass case demonstrates that the moment of inertia ratio is the dominant similarity parameter. This dominance appears as a five second difference in the point of instability. The thrusting case shows the negligible effects of the mass-flow-induced terms and the isentropic nozzle model for this set of trajectories (magnitudes [congruent to] 10⁻³). Also, the optimization of the mass properties before the thrust history significantly improves the performance of the vehicle (increased rotational tracking).