Relative Orbit Control Of Fractionated Spacecraft Based On Electromagnetic Force

In contrast with traditional thrusters, applying electromagnetic force to control therelative position of fractionated spacecraft modules provides significant advantages ofzero fuel consumption and plume contaminations elimination. However, it also bringsenormous challenges of strong coupling and nonlinearity. In this thesis, the control ofelectromagnetic force in the application of fractionated spacecraft modules’ relativeposition is studied systematically, and mainly including the following sections:The electromagnetic force’s far-field model and near-field model are established,and by mathematical simulation, the error of far-field model, which is more applicablefor control design, is analyzed. The results show that the far-field model error decreaseswith the increase of the coil distance. Then the relative orbital dynamics are derivedbased on a virtual satellite, then the mathematical simulation validates that theelectromagnetic force’s influence on the equations of motion can be neglected.In this section, applying the free dipole, the current decoupling control model oftwo satellites’ formation with the assumption of attitude coordination is derived firstly.Then based on the uncertainty matching model of electromagnetic force’s error, therelative orbit tracking control of two satellites formation by electromagnetic force isachieved with the sliding mode control algorithm. Following the analysis of thesingularity problem of the sliding mode relative orbit control law, two free dipolestrategies are proposed to solve the singularity problem, namely the switching strategyand aligning strategy. The simulation results show that the proposed sliding modecontrol law with electromagnetic force can track the relative orbit of two satellitesformation, whether applying the switching strategy or the aligning strategy.In this part, the multi-satellite coupling control problem with electromagnetic forceis decomposed into the decoupling control design sub-problem, in which theelectromagnetic force is the direct control input, and the sub-problem of magneticdipoles distribution. Firstly based on the parameterized electromagnetic force error,applying the adaptive control algorithm to estimate the far-field error parameters online,and derive the desired electromagnetic force. Meantime, the algorithm’s stabilitywithout disturbance and the ultimate boundedness with disturbance are certificated viaLyapunov stability theory. Then the projection method is adopted to avoid parameterdrift. Lastly the magnetic dipoles optimal distribution is achieved by the nonlinearoptimization method, which is to reduce the energy consumption and improve thecontinuity of solutions. The simulation results have showed that the adaptive controllaw which is regarded electromagnetic force as the direct control input can track the relative orbits of the multi-satellite formation, and the magnetic dipoles are evenlydistributed by the nonlinear optimization method.In the last section, the limitations of the reconfiguration targets which is achievedby electromagnetic force is analyzed firstly. Then for the dynamic target configuration,applying the artificial potential field method to derive the reconfiguration control law,and the terminal convergence rate is increased by the improved potential function.Lastly for the static target configuration, adopting the refined switching controlalgorithm avoids the local minima problem. The simulation results have showed that theproposed reconfiguration control law based on the artificial potential field method canreconfigure satellites formation by the electromagnetic force, and the maneuvering timecan be reduced via the terminal acceleration potential function, besides, the switchingcontrol law can avoid the local minima problem.