Dynamics and real-time optimal control of satellite attitude and satellite formation systems

摘要

In this dissertation the solutions of the dynamics and real-time optimal control ofmagnetic attitude control and formation flying systems are presented. In magneticattitude control, magnetic actuators for the time-optimal rest-to-rest maneuver with apseudospectral algorithm are examined. The time-optimal magnetic control is bang-bangand the optimal slew time is about 232.7 seconds. The start time occurs when themaneuver is symmetric about the maximum field strength. For real-time computations,all the tested samples converge to optimal solutions or feasible solutions. We find theaverage computation time is about 0.45 seconds with the warm start and 19 seconds withthe cold start, which is a great potential for real-time computations. Three-axis magneticattitude stabilization is achieved by using a pseudospectral control law via the recedinghorizon control for satellites in eccentric low Earth orbits. The solutions from thepseudospectral control law are in excellent agreement with those obtained from theRiccati equation, but the computation speed improves by one order of magnitude. Numerical solutions show state responses quickly tend to the region where the attitudemotion is in the steady state.Approximate models are often used for the study of relative motion of formationflying satellites. A modeling error index is introduced for evaluating and comparing theaccuracy of various theories of the relative motion of satellites in order to determine theeffect of modeling errors on the various theories. The numerical results show thesequence of the index from high to low should be Hill's equation, non- J2, smalleccentricity, Gim-Alfriend state transition matrix index, with the unit sphere approachand the Yan-Alfriend nonlinear method having the lowest index and equivalentperformance. A higher order state transition matrix is developed using unit sphereapproach in the mean elements space. Based on the state transition matrix analyticalcontrol laws for formation flying maintenance and reconfiguration are proposed usinglow-thrust and impulsive scheme. The control laws are easily derived with highaccuracy. Numerical solutions show the control law works well in real-timecomputations.