Optimal trajectories of reentry vehicle by serial and asymptotic matching.
Dongsuk Han · Deep Blue (University of Michigan) · 1993
With the advent of aeroassist technology for orbital transfers, it is of interest to have explicit optimal control laws for aerodynamic control during atmospheric passage of the space vehicle. Due to the nonlinearity of the equations of motion, the exact analytic solutions are not available. Previously, analytic solutions were available only for the simplified problems, usually separated into two different regions, namely, for the orbital flight and atmospheric flight. In this thesis, an analytic optimal control law uniformly valid in both regions is obtained. The differential equations for the optimal lift control coupled with the state equations can be fully integrated analytically by neglecting either the gravity or the aerodynamic force terms. A serial matching technique for the skip trajectory is proposed using the two controls obtained in these two separate regions. The switching condition between the two controls is derived and the solution is compared with the exact solution for a sample trajectory. This technique shows a good estimation of the cost function and provides a good physical explanation of the lift control as well. A matched asymptotic expansion method is used, coupled with the full knowledge of the physical properties of the exact integrals of motion, to derive the explicit optimal control laws for lift and bank modulation during the entry phase. The results from this control strategy by the matched asymptotic expansion method are compared with the exact numerical solutions for a variety of skip and glide entry trajectories. Its performance is excellent in the sense that the control exhibits the same characteristic behavior as the exact solution and it also leads to nearly the same cost function.