On the synthesis of dynamics and control for complex multibody systems

This dissertation develops in a unified manner a new and simple approach for the modeling and control of complex multibody systems. Complex multibody systems are those nonlinear mechanical systems consisting of individual subsystems that are describable by nonlinear differential equations. The interaction of the various subsystems is, in general, governed by nonlinear 'elements.' The nonlinear analysis of general multibody systems presents theoretically challenging problems in both its dynamics and controls aspects. The theoretical developments obtained in this dissertation permit the modeling of multibody systems so that no restrictions are imposed in its formulation, except that its physical model is continuous. The idea of permissible multibody control is developed, and an effective method is provided for generating nonlinear controllers that satisfy a general set of control objectives.;The generalized acceleration describing the rotational motion of a rigid body in terms of quaternions is directly obtained thus providing a rotational description for the general motion of multibody systems. Utilizing this formulation, two new control strategies are obtained that explicitly yield the nonlinear control torque required to re-orient a rigid body from an arbitrary rest orientation to another arbitrary rest orientation. The application of this new approach to problems in complex multibody spacecraft systems is carried out for spacecraft precision pointing and to the precise tumbling control of an elastically connected multibody spacecraft system. Numerical examples are provided showing the ease of implementation of the methodology and the accuracy with which the control objectives are satisfied. These results illustrate the capability to easily generate physical models and provide exact control of highly nonlinear, complex multibody systems.