Active Control Schemes to Satisfy Separation Distance Constraints
| Autor: | Pedro A. Capó-Lugo, Peter M. Bainum |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Elliptic orbit
Applied Mathematics Aerospace Engineering Function (mathematics) Linear-quadratic regulator Optimal control Space and Planetary Science Control and Systems Engineering Orbit (dynamics) Benchmark (computing) Tetrahedron True anomaly Electrical and Electronic Engineering Algorithm Mathematics |
| Zdroj: | Journal of Guidance, Control, and Dynamics. 30:1152-1156 |
| ISSN: | 1533-3884 0731-5090 |
| DOI: | 10.2514/1.24371 |
| Popis: | T HE proposed NASA benchmark tetrahedron constellation is a complex formation to be maintained at every apogee point. In previous papers, the authors developed a strategy and determined the initial conditions to maintain the tetrahedron formation [1,2]. With this strategy, the constellation maintains the separation distance constraints for a limited number of orbits, depending on the specific size of the NASA benchmark problem [3]. After a pair of satellites violates the separation distance constraints [1,2], a control strategy is needed to maintain the separation distance conditions [3]. The NASA benchmark problem [3] establishes that the nominal separation distance between any pair of satellites within the constellation is 10 km at the apogee point, and, at any other point in the orbit, the separation distance cannot be less than 1 km. To explain the dynamics of a pair of satellites in an elliptical orbit, the linearized Tschauner–Hempel (TH) equations are used. In the TH equations, the coefficient term that varieswith the true anomaly angle will affect the control scheme that is used to maintain the separation distance between a pair of satellites. The control strategy is based on the linear quadratic regulator (LQR) which was used by Bainum, Strong, and Tan (BST) [4–6]. These authors used the LQR control scheme to maintain the separation between a pair of satellites in an along-track formation (string of pearls), and the varying coefficient was adapted in a piecewisemanner. Instead, Carter–Humi (CH) [7,8] used a different approach in which the cost function is defined in terms of the true anomaly angle, and this control scheme will be adapted here to the LQR strategy. These two control schemes will be compared to determine the best response from the BST and CH control approaches. After the constellation is corrected, the Satellite Tool Kit (STK) [9] software is used to propagate the constellation motion and determine when the constellation will again violate the separation distance constraints. Hence, the main objective of this engineering note is to compare and apply these two techniques for the first time to the NASA Benchmark Tetrahedron Constellation to correct the violation of the separation distance constraints [3]. II. Definition of the Specific Sizes (or Phases) |
| Databáze: | OpenAIRE |
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