Optimal Mars Entry Trajectories for Bank-Angle and Alpha-Beta Steering

This study formulates and solves a number of optimal control problems for a Mars entry vehicle in order to summarize the command profiles needed to meet different trajectory objectives. Optimal control problems are solved for both vehicles using bank-angle steering and alpha-beta steering during hypersonic flight, providing a flight performance comparison between these two steering schemes as well as a better under standing of alpha-beta steering. The optimal control problems considered are solved using direct-based pseudospectral methods and include the maximum altitude, minimum control effort, minimum error, minimum heat load, as well as the minimum peak heat rate, dynamic pressure, and aerodynamic load problems.While flight performance of alpha-beta and bank-angle steering is found to be similar among most of the objective functions considered, alpha-beta steering is found to provide terminal altitudes about 0.5 km higher than bank-angle steering. Results also indicate alpha-beta steering is much less sensitive to decreases in maximum vehicle rotational rates, relative to bank-angle steering, when terminal altitude is being optimized. Results show bank-angle steering leads to values up to 4.4%, 3.3%, and 1.4% higher than alpha-beta steering, for the heat load, peak heat rate, and peak dynamic pressure, respectively, indicating improved performance for alpha-beta steering. The structure of optimal command profiles also demonstrates qualitative differences between these two steering options. For example, the minimum control effort problem shows that a vehicle using alpha-beta steering can fly to the terminal target with a constant alpha-beta profile, whereas a bank-angle steering vehicle generally must have at least one bank reversal.