Dynamics And Control Of Electromagnetic Satellite Formation

Satellite formation flying has a number of benefits during space missions that are difficult to accomplish using a single large spacecraft. Employing a group of satellites can significantly enhance reliability because each member is replaceable, and a fault in one vehicle may not severely endanger the formation and the mission. Electromagnetic Formation Flight(EMFF) is a relatively new concept of no-fuel-consumed formation flying that has been proposed to remove the limitations and shortcomings imposed by propellants. In EMFF, each satellite is equipped with three large orthogonal coils that generate electromagnetic forces. The relative satellite positions are then determined by these electromagnetic forces, while attitudes are controlled via reaction wheels or control moment gyros. The electromagnetic coils and attitude actuators are all powered by solar arrays, and the mission lifetime is theoretically unlimited. This thesis studies the dynamics and control issues in EMFF, and the considerations are listed as follows.First, the generally applied electromagnetic force approximation is not very accurate in a close distance, and its form is complex and not appropriate for control design. To improve accuracy, a modified far-field electromagnetic force mode is proposed by retaining high order terms in the Taylor series of field-source position vector. Then, a directional magnetic dipole allocation is introduced to simplify the modified far-field model. With the directional dipole allocation, the influence of current to electromagnetic force is distinct, which is helpful to the control design. Analysis is given to show the effectiveness of modified far-field model with directional magnetic dipole allocation from accuracy, efficiency and torque allocation.Second, the maximum current density in conductors is limited, which inevitably imposes input saturation on control design. Considering the requirement of rapid configuration for satellite formation, the fast trajectory tracking with input saturation is an interesting issue. Two control methods are proposed under the framework of sliding mode control. The first one is designed based on the estimate of maximum saturation degree and terminal sliding mode surface; the second one is achieved through introducing a modulation function, and allows for maximum input and removes chattering. Both methods can deal with input saturation, disturbance and uncertainty.Third, the translational dynamics of EMFF is highly coupled, and it is difficult to design a controller for one satellite without considering the state and input of others, which poses additional challenges to magnetic dipole determination. The decoupling control methods applying frequency division are studied in this paper. The problem caused by frequency division is discussed through presenting an example of learning-based sliding mode control, and two methods are investigated to solve this problem. The first one is imposing input rate saturation and designing a LMI based control; the second one is introducing a feedback filter to guarantee the effectiveness of frequency division. Compared with the optimization method, the second way gains flexibility and simplicity.Fourth, an electromagnetic field used also creates an electromagnetic torque on each vehicle. This associated torque can only be offset by attitude actuators, which inevitably leads to persistent angular-momentum buildup. A group of parameters are introduced to represent the relation between the electromagnetic force and torque. These parameters enable a certain freedom of allocating electromagnetic torques, and help find an analytical dipole solution to minimize total electromagnetic torque action. Torque-free formations are also investigated, and a parameter optimization model is derived under the framework of sliding mode control to minimize angular-momentum buildup.Finally, a complete angular-momentum management and control scheme is proposed to dump angular-momentum build up of systems while simultaneously achieving accurate trajectory tracking. The proposed scheme combines alternating current with direct current to create an integrated magnetic dipole. The alternating component in the final input dipole is used to control the relative positions of the spacecrafts, while the constant component interacts with the geomagnetic field to reduce the unbalanced and excessive accumulation of angular momentum in the formation system. Thus, angular-momentum management can be decoupled from the trajectory control design, thereby removing restrictions on the dipole solution.