Dynamics and control of evolving space platforms: An approach with application

A relatively general formulation for studying dynamics and control of a large class of space systems is developed. The formulation has the following distinctive features: (a) it is applicable to an arbitrary number of beam, plate, membrane and rigid body members, in any desired orbit, interconnected to form an open branch-type topology; (b) joints between the flexible members are considered rigid permitting arbitrary large angle rotation and linear translation between the structural components; (c) symbolic manipulation is used to synthesize the nonlinear, nonautonomous and coupled equations of motion thus providing an efficient modelling capability with optimum allocation of computer resources; (d) the governing equations are programmed in a modular fashion to isolate the effects of appendage slewing and translation, librational dynamics, structural flexibility and orbital parameters; (e) both the nonlinear and linear forms of the equations of motion have been formulated and programmed to help assess relative performance of various control strategies with reference to linear as well as nonlinear dynamics.

The above multibody dynamics formalism involves representing structural deformation in terms of system modes. This feature has several advantages: the formulation effort and derivation time are dramatically reduced; the complexity of the governing equations of motion is considerably simplified; the terms representing structural flexibility contributions are decoupled due to orthogonality of the normal modes with respect to the mass and stiffness matrices; and the physical interpretation of the results becomes more meaningful, since the modal frequencies represent resonance conditions for the overall structure. For geometrically time varying systems, the modes are updated at user specified intervals, thus maintaining a faithful representation of structural flexibility throughout the simulation sequence. Furthermore, the finite element method used in the calculation of system modes makes the present algorithm ideal for visualization of the spacecraft dynamics and control through computer animation. A video depicting modal interactions of the evolving Space Station has been produced in collaboration with the University Computer Services Visualization Group.

Applicability and versatility of the general formulation are illustrated through the analysis of two evolutionary stages of the Space Station: the First Milestone Configuration and the Assembly Complete Configuration. Effects of the number of system modes, and operational disturbances (solar panel sun tracking, Orbiter docking, crew motion and manipulator tasks) are investigated. Control strategies using both linear and nonlinear dynamics have been implemented and their relative performance compared. It is shown that the controller imparts the Space Station, which has a gravitationally unstable orientation, a desired degree of stability. The simulation results represent important information and may help in defining the design loads for the Space Station's main truss structure, solar arrays, modules and other secondary components.

Summarizing, the unique feature of this study is evident in the development of an interdisciplinary integrated algorithm synthesizing multibody dynamics, finite element method for modal discretization, symbolic manipulation, application of linear and nonlinear control approaches, and computer animation.