Algorithm On Satellite Formation Keeping Along Eccentric Orbit

Satellite formation flying has been paid great attention for its unique techniqueadvantages such as low-cost, high performance and autonomous. Formation flyingalong eccentric orbits has more advantages over the circular ones, as it increases thecoverage interval by locating the apogee just above the target area, which improves theefficiency of the satellites. Formation keeping is necessary for the existence ofperturbation and initial error, which deviates the orbit from the predetermined one.Moreover, formation keeping is also the foundation of all the formation control issuesas every single operation needs to achieve stability by formation keeping controlstrategy. This thesis is focused on formation keeping control along eccentric orbits, andthe main contents and contributions of this thesis are summarized as follows:(1) The equation for the relative motion expressed in the orbit coordinate of thetarget satellite is established, and the model is then linearized into dimensionless formwith the true anomaly as the free variable by feedback linearization, variabletransformation. Moreover, the relation between the two models is proposed in detail,and the advantages and disadvantages of the two models are discussed. In addition, theexpression of the relative perturbation acceleration is presented.(2) The sliding mode control method is studied for the satellite formation keepingalong eccentric orbits with consideration of unknown bounded perturbation. Firstly, aglobal integral sliding mode controller is designed to improve accuracy and robustnessof perturbation changing based on the time-domain model, and both the position errorand velocity error are used as standards to measure completing the keeping task.Secondly, the sliding mode controller and adaptive controller are combined to achievethe estimate of the bound of the perturbation. Finally, take the advantages ofdimensionless model into account such as simple and without using positioninformation of target satellite, a linear sliding mode controller is designed based on thedimensionless model.(3) The backstepping control method is studied for satellite formation keepingalong eccentric orbits with consideration of known perturbation. Firstly, a statefeedback controller based on the method of backstepping is derived. Secondly, anoutput form is obtained by variable transformation. Based on this output form, a state estimator is designed to obtain the estimate of the relative velocity of the followerspacecraft and an output feedback law is derived for the relative position trajectorycontrol. Based on the Lyapunov approach, it is shown that the closed-loop system isglobally uniformly stable. Finally, a backstepping controller is designed based on thedimensionless model.(4) The neural network adaptive control method is studied for satellite formationkeeping along eccentric orbits with consideration of unknown perturbation. Firstly, theperturbation is expressed as the form of a function of neural network, and adaptive lawis designed to approximate perturbation, combined with a sliding mode law to achieve astate feedback controller. It can be demonstrated by Lyapunov theory that a necessaryand sufficient condition on the directed graph is presented such that the keeping errorcan be reduced as small as desired. Moreover, the control algorithm without usingrelative velocity information is proposed. Finally, the control effects of all the abovemethods are analyzed.