Stationkeeping Control Of Two-body Tethered Satellite System Around Colinear Libration Points

The space around Libration points is an ideal place for deep space exploration using satellite formation flying. Because of the advantage in formation maintenance and reconfiguration, tethered satellite system is suitable for some future libration points missions, such as the high angular resolution interferometry remote sensing. Since collinear libration points and orbits near them are inherently unstable, the stationkeeping control is of great importance for libration point spacecrafts. With the support of Chinese Science National Foundation – the dynamics modeling and control of tethered satellite system in deep space environment, this thesis studies the stationkeeping control of the two-body tethered satellite system near the colinear libration points. The main contents of this dissertation are as follows:First of all, under the assumption of circular restricted three-body problem, the stability of the two-body tethered satellite system is systematically studied. Based on the linearized model, the eigenvalues and the corresponding eigenvectors are caculated. At the same time, the impacts of the tether length variation on the stability of the system are also analysed through numerical method. Two different numerical methods, the differential correction method and the collocation method(Pseudospectra method), are employed in the design of periodic orbits around the colinear libration points. Furthermore, on the basis of the orbit initial states calculated by these two numerical methods, some periodic orbit families relating to the rotating tethered satelllite system are obtained by the continuation method. The dynamical analysis carried out by this thesis provide the fundamental results for the stationkeeping controller design while the orbits caculated through numerical methods are accurate reference orbits for the numerical simulation experiments.Secondly, the stationkeeping problem using low-thrust engine is studied. Without considering the control input saturation problem, two continuous control strategies are designed. Firstly, considering the fact that the controlled system is cascade, the backstepping procedure is carried out to design the stationkeeping controller. The controller is also modified to deal with the loss of velocity information by incorporating the velocity observer. Meanwhile, an output feedback backstepping controller are proposed for the rotating tethered satellite system. Secondly, the SDRE nonlinear optimal controller with θ-D technique is proposed to optimize the ΔV. Since the SDRE controller is inherently state regulator, two design methods are employed to make it capable of tracking dynamic signals. Finaly, taking into account the case that the space environment is very complex in the Earth-Moon system, the perturbed restricted three-body model is established, and the two controllers mentioned above are improved to suppress the influence of the space perturbation. Numerical simulation experiments are carried out to demenstrated the effectiveness of the proposed control strategies.Thirdly, still using the low-thrust engine as the actuator, the control input saturation problem are considered in the stationkeeping controller design. On the basis of backstepping control algorithm, an ‘observer-based’ anti-windup contrller modification is implemented by introduceing two auxiliary variables. Then, the nonlinear model preditive control technology is employed in the controller design procedure due to its inherent capability of taking constraints into account. Furthermore, because the model predictive control essentially solves standard optimal control problems, the optimization of ΔV is taken into considerantion naturally. Subequently, Tube-based nonlinear model predictive controller is proposed to obtain recursive feasibility and robust stability for control mission with state constraints in the Earth-Moon system. Both of the collocation method and robust backstepping technology are incorporated into the robust controller design procedure. The effectiveness of the controller designed above are validated through numerical simulations considering the actuator limits.Subsequently, the variation of tether length are considered in the controller design. First, The dynamic controll allocation technique are emplied to incorporate the impact of tether into stationkeeping control, as well as considering the teher length as one control input in the model predictive control. Next, using tether as the sole control input, a dynamical approach based on the dynamic property of the rotating tethered satellite system is proposed for the colinear libration point stabilization control. Furthermore, based on the Floquet mode, an efficient stationkeeping strategy for the periodic orbit is derived considering the natural dynamics of the rotating tethered satellite system around the colinear libration points. Finaly, the performance of the control algorithms proposed above is checked in the numerical simlations.Finaly, due to the importance of accuracy in the simulation experiments, ephemeris data is employed to examine the behavior of the controllers proposed in this thesis. The high-accuracy ephemeris model for rotating tethered satellite system in the J2000 inertial coordinate system is established in the Earth-Moon system. Quasi-periodic orbits are generated by applying the multi-shooting method. Both the colinear libration point stabilization control and quasi-periodic orbit stationkeeping control are simulated under the action of backstepping controller, SDRE controller and nonlinear model predictive controller. Simulation results reveal that although each control scheme has its own advantages and disadvantages, all of them are capable of maintaining the rotating tethered satellite system in the vicinity of the target position for a considerably long period. The selection of the appropriate stationkeeping controller should corespond with the specific mission requirements.