Research On Inner Formation Orbit Keeping Control Methods

Pure gravity orbit spacecraft flies with the effect of gravity only. Its orbit reflects the variation of gravity field. A high precision and high resolution gravity field model can be achieved through analyzing orbit data of pure gravity orbit spacecraft. The inner formation satellites, including inner satellite and outer satellite, which fly in formation, are used in gravity field measurement. Inner satellite is a proof mass, flying in the cavity of outer satellite. In nominal state, inner satellite is in the center of outer satellite. Those nonconservative forces such as atmospheric drag and solar radiation pressure are shielded by outer satellite. Inner satellite flies in pure gravity orbit. Outer satellite follows inner satellite accurately. The accurate orbit of inner satellite can be achieved through measuring relative position between inner satellite and outer satellite and determining orbit of outer satellite with high precision. Inner formation orbit keeping control system, which is very important for accomplishing the mission of detecting gravity field, keeps inner satellite flies in the center of the cavity of outer satellite. Inner formation orbit keeping control is a control problem with strong disturbances. Inner formation orbit keeping control methods are studied based on inner formation satellites.Firstly, the research backgrounds are introduced. The research states of both formation configuration keeping control technologies and Drag-Free control technologies are summarized. The application aeras of Drag-Free control technologies are similitude to those of inner formation configuration keeping control.Secondly, inner formation orbit keeping control system models are introduced. Inner formation satellites'mission requirements and parameters are proposed. Dynamical equations are set up. And disturbances are analyzed.A traditional PID control is investigated based on inner formation satellites. A nonlinear PID controller is designed by adding a nonlinear item to traditional PID control, concluding that gains of nonlinear PID control vary with control process. Both traditional PID control and nonlinear PID control of inner formation satellites are simulated. And results show that both of them keep the relative position between inner satellite and outer satellite in the desired range. Nonlinear PID control converges more quickly than traditional PID control. The control capabilities of traditional PID controller and nonlinear PID controller are analyzed when there is an error in mean angular velocity of orbit. Results show that both of them can ensure inner formation satellites fly steadily. The control abilities of traditional PID controller and nonlinear PID controller are investigated when there is a mutation in relative state between inner satellite and outer satellite. In simulation conditions of this paper, nonlinear PID controller make formation satellites fly steadily, while traditional PID controller can not. The control abilities of traditional PID and nonlinear PID are studied when there are measurement errors. Results show that both of them can fulfil relative position control requirements, while the precisions of steady relative position reduce.Thereafter, an inner formation model predictive control method is proposed. An approach of solving model predictive control problem is introduced. The inner formation model predictive control is simulated. And results show that model predictive control method, which keeps inner formation satellites flying steadily, is suitable for inner formation orbit keeping. The relationship between weight coefficient and steadt relative position error is investigated. The control capability of model predictive control is analyzed when there is an error in mean angular velocity of orbit. The results show that model predictive control can ensure inner formation satellites fly steadily. The control ability of model predictive controller is studied when there are measurement errors. Results show that model predictive controller can fulfil relative position control requirements, while the precisions of steady relative position reduce. But the precisions of steady relative position are still higher than that of PID controller.Finally, an inner formation model predictive PD control is proposed. In comparation, the convergent time is long and the values of control accelerations are small for model predictive control, and the convergent time is short and the values of control accelerations are big for PID control. A new control is designed by combining model predictive control and PID control. Results show that the convergent time is much shorter after that a PD term is included in the control system. And the values of control accelerations of model predictive PD control are smaller than those of PID control. Model predictive PD control is suitable for inner formation satellites. The control capability of model predictive PD controller is studied when there is an error in mean angular velocity of orbit. Results show that model predictive PD controller makes formation satellites fly steadily. The control ability of model predictive PD controller is studied when there are measurement errors. Results show that model predictive PD controller can fulfil relative position control requirements, while the precisions of steady relative position reduce. The order of magnitude of model predictive PD control is the same as model predictive PD control. But the precisions of steady relative position are still higher than that of PID controller.