Effect of Initial Flight Path Angle Error and Control Constraint on the Optimized Ascent Trajectory of a Typical Launch Vehicle

Abstract

The present paper investigates the effects of Initial flight path angle error and Constraints on the permissible angle of attack, on the optimal ascent trajectory of a typical two stage launch vehicle. The problem is formulated as an optimal control objective and the standard steepest descent technique is used for generating the optimal trajectory. The guidance command history is generated as the solution for ensuring the desired terminal conditions are met with the minimum control effort and minimum structural loading in the high dynamic pressure region. In this study, the angle of attack is used as the guidance control variable and the optimal profile for angle of attack is generated for four different terminal conditions, under the specified constraints. Two cases are considered, one in which launch vehicle has a small error in its initial flight path angle and the other, in which the control input is constrained to within ±5 deg.The results show that while the terminal constraints are met exactly, there is a significant change in the angle of attack profile for both initial flight path angle error and the maximum angle of attack constraint. Based on these results, a method for analytically predicting the optimal control profile is proposed.