Digitial LQR Control Scheme to Maintain the Separation Distance of the NASA Benchmark Tetrahedron Constellation

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

“…Bainum, Strong, and Tan (BST) [5][6][7] developed a piecewisely adaptive scheme to maintain the separation distance conditions for an along-track constellation. Their approach was applied to the NASA benchmark tetrahedron constellation [4], but this scheme was constrained by the eccentricity of the orbit; in addition, the BST control scheme depends on the weighting matrices because, for one of the specific sizes of the benchmark problem, the eccentricity constraint can be avoided [4].…”

“…This active control scheme was based on the linear quadratic regulator (LQR) expressed continuously in the true anomaly angle [4]. With this LQR active control scheme, two different control approaches were studied to maintain the separation distance constraints at the following apogee point after the first pair of satellites have violated the separation distance conditions [4]. Bainum, Strong, and Tan (BST) [5][6][7] developed a piecewisely adaptive scheme to maintain the separation distance conditions for an along-track constellation.…”

“…After a pair of satellites within the constellation violates the separation distance conditions, an active control scheme is needed to satisfy the separation distance constraints of the NASA benchmark problem [2]. This active control scheme was based on the linear quadratic regulator (LQR) expressed continuously in the true anomaly angle [4]. With this LQR active control scheme, two different control approaches were studied to maintain the separation distance constraints at the following apogee point after the first pair of satellites have violated the separation distance conditions [4].…”

Formation flying control implementation for highly elliptical orbits

“…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 main advantage of the discrete systems is that the computational time can be reduced by selecting a suitable sampling interval. For this digital system, the amount of data will depend on the sampling interval in the true anomaly angle [3]. The purpose of this paper is to implement the discrete Tschauner-Hempel equations and the steady-state hierarchical controller in the computer onboard the satellite.…”