Steady-state hierarchical control for the drift correction of a constellation in highly elliptical orbits

Abstract

The hierarchical control scheme is used to obtain the solutions of two-point boundary value problems to correct the separation distance drifts of a pair of satellites within a constellation in highly elliptical orbits according to mission constraints. One of these solutions is the drift correction that shows a faster correction than the solution of the two-point boundary value problem for the station-keeping process of a pair of satellites within a constellation. For the drift correction, the hierarchical control scheme uses an iterative method to obtain the solution for the drift correction. Thus, the hierarchical control scheme is re-expressed as a steady-state system to reduce the computational process and time. In summary, the steady-state hierarchical control scheme is used to correct the drift between a pair of satellites within a constellation in which the computational process is minimized.

Formation flying control implementation for highly elliptical orbits

“…In reference [2], the discrete TH equations for a perturbed motion that defines the motion of a pair of satellites in an elliptical orbit about the Earth can be described as,…”

“…x is positive against the motion of the spacecraft, 2 x is positive along the radial direction, and 3 x is positive when the right handed system is completed. The j y equations are used as a mathematical transformation.…”

“…The steady-state hierarchical control scheme was implemented with the cost function defined in Ref. [2]. In steady-state [2], the control problem can be reduced and defined in the following form,…”

“…In reference [2], a block diagram for the steady-state hierarchical control scheme was developed. This block diagram can be easily modeled in the computer onboard the satellite.…”

“…This set of equations was discretized in the true anomaly angle [1] to be used in a digital steady-state hierarchical controller [2]. This controller [2] performed the drift correction between a pair of satellites within the constellation. The objective of a discretized system is to develop a simple algorithm to be implemented in the computer onboard the satellite.…”