Digital LQR control scheme to maintain the separation distance of the NASA benchmark tetrahedron constellation

In previous papers, the authors developed an active control scheme based on the linear quadratic regulator (LQR) to maintain the separation distance constraints of the NASA benchmark tetrahedron constellation. Two different active control schemes were used to maintain the separation distance constraints, but one control scheme applied to every eccentricity of the NASA benchmark problem. Through this paper, the digital LQR strategy will be developed with this active control scheme to maintain the separation distance conditions of the tetrahedron constellation. The motion of a pair of satellites in an elliptical orbit about the Earth is defined by the linearized Tschauner-Hempel (TH) equations. These equations will be defined discretely in the true anomaly angle for the development of the digital control scheme. In summary, the digital LQR approach will be implemented and studied to determine how this active control scheme maintains the separation distance constraints for different specific sizes of the NASA benchmark tetrahedron constellation.