Abstract
I NHIGHLY elliptical orbits (HEO), the solar pressure can perturb themotion of a constellation because of the longer exposure of the satellites to the sun [1]. To study its effects on the controller, the Tschauner–Hempel (TH) equations are augmented to include the effects of the solar pressure force. These TH equations are also expressed to include the effects of the perturbation due to the oblateness of the Earth (or J2 perturbation) [2]. To formulate this problem, theCarter–Humi (CH) approach [3] is used inwhich theTH equations are expressed in terms of the eccentricity and the true anomaly angle. These terms are important for the development of the control scheme [4–6]. The TH equations contain nonlinear terms due to the J2 perturbation [2] that can be considered in the controller. Capo-Lugo and Bainum [2] developed a hierarchical control scheme, in discrete format, to maintain the separation distance constraints for the nonlinear TH equations. This controller is based on the linear quadratic regulator and compensates for these nonlinear effects. The solar pressure force is only dependent on the position of the satellite but can affect the control effort. In conclusion, this paper shows how the solar pressure effects can cause variations in the control effort for the correction of the separation distance constraints for a pair of satellites within a constellation.
Published Version
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