Nonlinear Attitude Control And Optimal Guidance Of Spacecraft

This dissertation includes research of nonlinear attitude control of spacecraftand optimal guidance for soft landing of lunar module. It can be divided into twoparts: in the first part nonlinear attitude controls of spacecraft based on scissored pairof control moment gyros or double gimbal control moment gyros are studied; in thesecond part precise modeling, the optimal guidance and optimal trajectory design forlunar module soft landing are studied.The combination of a pair of gyros which could precess synchronously withinone gimbal is called scissored pair of control moment gyros, where the two gyrosmust synchronously precess for proper momentum exchange with the spacecraft. Soour aim is to design a controller which could guarantee the two gyros to precesssynchronously. To suppress external disturbances to the system, we design anonlinear feedback controller by using the method of feedback linearization,backstepping Lyapunov theory and young’s inequality. It can be proved that if theunknown disturbances are bounded, then the tracking error and the synchronizationerror are all bounded. Furthermore, the nonlinear tracking dynamics of the system areproved to be bounded in the case of a bounded command.Concerning both unknown inertia properties and unknown constant disturbances,we propose an adaptive control law for the closed-loop slewing motion controlutilizing the methods of feedback linearization, backstepping tuning function andLyapunov theory. Under this design the system tracking error and thesynchronization error converge to zero. The proposed nonlinear control law based onscissored pair of control moment gyros can be applied to many kinds of spacecraftssuch as lunar orbit module, space station and space platform.Concerning the attitude control of three axis large angle maneuver of spacecraft,we derived an exact mathematical description for the angular motion driven bydouble gimbal control moment gyros. A nonlinear control law is designed based onthe second method of Lyapunov. System capabilities to avoid or withdraw from thesingularity are studied under different steering laws. Moreover, a theorem about thesingularity of double gimbal control moment gyros’ system is proposed. Based onthis theorem the singularities of two configurations of double gimbal control momentgyros system are detailed. The first configuration consists of three orthogonally mounted double gimbal control moment gyros and the second configuration consistsof four parallel mounted double gimbal control moment gyros. Simulation resultsshow that both the two configurations can effectively fulfill tasks of trackingconstant torque commands and driving large angle attitude maneuvers, even some ofthe gyros fail in both the two configuration. The system dynamics and nonlinearcontrol law proposed for double gimbal control moment gyros can be applied toattitude control of lunar orbit module, lunar descent module and some other kinds ofspacecrafts.Three dimensional dynamics for lunar module soft landing were presented byintroducing two sets of coordinate without consideration of the moon rotation. Inpractice, the thrust of the module always works in switching mode which can not beadjusted smoothly. We assume that the attitude commands can be followed precisely.To realize the minimal fuel strategy, an optimal open loop guidance law is proposedbased on the maximum principle. By solving the two-point boundary value problemwith the constraints of final velocities, the optimal trajectory of the lunar soft landingis obtained.To enhance the precision of soft landing which would be influenced by themoon rotation, we introduce another coordinate, Lunar Centered Fixed Coordinate,and a precise three dimensional dynamic model with consideration of the rotation ofmoon is then derived. Using the minimal fuel consumption as an index, we present anopen loop optimal guidance law based on Pontryagin’s maximum principle. Optimaltrajectories are obtained by solving the two-point boundary value problem withconstraints of final velocities and locations.By introducing two new state equations, the system dynamics obtainedpreviously can be changed which would have the form of affine nonlinear systems.Based on the new equations, a closed loop optimal guidance law is designed with aparameter matrix K to be determined which is the solution of a riccati likedifferential equation. Here we propose a more practical method to calculate thematrix K that is to let the closed loop controller approximate the numerical solutionsobtained by an open loop optimization, such that it is avoided to solve the complexriccati like differential equation.