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