Time Optimal Control For Three-axis Stabilized Satellite Reorientation

With the advanced development of spaceflight science and technology, thesatellite has been further applied to various fields of our life. When the satelliteperform disaster warning, detection scientific and military applications and other tasks,often requiring satellite attitude control system to provide the appropriate controlmoment, make the satellite from the current attitude maneuver to a given expectationsin the shortest time. It is a classic optimal control problem, but due to the satellitedynamics and kinematics equation is nonlinear and coupling, that is very difficult tosolve with traditional methods. In order to solve this problem, this paper made athorough research and the system simulation.Firstly, choosing the Rodrigues parameter method, which has no singular problemsand facilitate numerical algorithm of the correction, to describe the attitude of thesatellite movement. Proposed the complete mathematical description of three-axisstabilized satellite attitude maneuver time optimal control problem. For three-axisstabilized satellite attitude maneuver time optimal control problem can’t adopttraditional calculus of variations or minimum modulus principle to solve the problem,respectively adopt two kinds of numerical methods, gives the numerical solution oftime optimal attitude maneuver problem. One is direct discretization by geneticalgorithm, another kind is Gauss pseudo-spectral method. Both methods are numericalsimulated and validated, and the results are analyzed, illustrates the characteristics ofthe time optimal solution.Secondly, using two optimal control method associate with practice of satelliteengineering, for the angular velocity and angle constraints may appeared in satelliteengineering practice, obtaining the optimal control which satisfy the state constraint.Focus on the case of satellite actuators are redundancy that can impact on solving thetime optimal control, by rewriting the satellite attitude motion equation, successfullysolve and obtain the satellite attitude maneuver time optimal control and optimaltrajectory in the case of several typical configurations of actuator. The results showthat under case of actuators with more complex torque spatial constraints, time optimalcontrol switched between vertices in the torque spatial.Finally, considering the constant interference and periodic interference may existed in the environment of satellite project, established the satellite attitude dynamicequation of error and kinematic equation of error for attitude error of three-axisstabilized. According to the equation of error of the optimal trajectory trackingcontroller was designed, and, the controller is reconstructed by using sliding modevariable structure control method, and the different simulation results withoutcorrection control law and with correction control law in the Simulink is given. Theclosed-loop control is verified the effectiveness of the law on the optimal trajectorytracking.