Linear multivariable compensator design for flexible structure satellite

Abstract

The kinematic model of a body is a system of equations that define the position in space of each particle of the body from the values of a set of variables. The time variation of these variables describes the motion of the body. After, we review the different ways to describe the rigid motion and how to express all the kinematic variables and their time derivatives that we need later to formulate the dynamics. Finally, the kinematics of the flexible body are described by adding a set of deformation functions on to the rigid body kinematics, Many multibody dynamics software are available to build such kind of models but they address the nonlinear behavior and they are too much loud to be handled at the early prototyping phase. in the present work we starts by defining the metaheuristic optimization algorithm used later in PID tuning and after that we have two linear aproche the direct state space methode with three degree of freedom and free hybrid model with six degree of freedom after that in each model we apply the diffirent control thecnique proposed, this fact leads clearly to an improvement of the pointing accuracy. finaly a comparative stady between the two aproaches.