Dynamics and Control of Attitude, Power, and Momentum for a Spacecraft Using Flywheels and Control Moment Gyroscopes

Summary of Results The purpose of this research is to obtain algorithms for simultaneous control of the orientationof an Earth-pointing spacecraft, the energy stored by counter-rotating flywheels, and the angularmomentum of the flywheels and control moment gyroscopes (CMGs) used together as an integratedset of actuators for attitude control. Three important classes of motion relative to a local-vertical-local-horizontalreferenceframe L areexamined. Thefirstinvolvesmaintainingatorqueequilibriumattitude (TEA), in which angular momentum of the actuators remains small and cyclic. In thesecond, attitude is held fixed, resulting in secular growth in angular momentum and eventualsaturation of the momentum exchange devices. The third consists of a large-angle reorientationfrom one attitude, fixed in L ,toanother.In order to construct control laws and evaluate their performance with numerical simulations,dynamical equations of motion for a multibody spacecraft containing flywheels and CMGs arederived using Kane’s method, and expressed in vector-dyadic form. Each device is modeled as arigid axisymmetric rotor; the spin axis of a flywheel is regarded as fixed in the spacecraft, whereasthe spin axis of a CMG is not. The equations are nonlinear, and completely general with regardto the number and orientation of flywheel rotors, and the number of CMG rotors and gimbals.A set of twelve scalar equations is obtained by applying the generic relationships to the specialcase of a complex gyrostat consisting of a base body and three pairs of flywheels mounted inorthogonal directions. Existing literature contains equations for describing motion of a spacecraftwith CMGs; they are shown to follow from the generic ones under two reasonable assumptions,namely that gimbal speeds are much less than the rotor spin speed, and reorientation of CMGrotors (and gimbals) does not significantly redistribute system mass. The exact equations for thecomplex gyrostat, and the approximate relationships associated with CMGs are combined to formapproximate equations for a spacecraft with flywheels and CMGs, and subsequently linearized andnondimensionalized in preparation for design of linear control laws.We develop two steering laws whose purpose is to determine the flywheel motor torques neces-sary to meet the attitude control and power management requirements simultaneously. The firstof these involves formation of a pseudo-inverse to solve an underdetermined system of equations byminimizing the sum of the squares of flywheel motor torques, whereas the second divides the powerrequirements evenly among the three pairs of rotors, resulting in a uniquely determined solution.Several laws are designed with the Linear Quadratic Regulator technique to control the first twotypesofmotion described heretofore, seeking and maintaining TEA, and holding an attitude fixed.Controller performance is illustrated through numerical simulations involving the InternationalSpace Station (ISS). Energy storage is shown to be affected adversely by damping of the flywheelrotors, whichmustbeexpectedunderrealisticconditions, buttheproblemiseliminatedbyfeedback76