MODELING AND CONTROL OF A FLEXIBLE SOLAR-ARRAY PADDLE AS A CLAMPED-FREE-FREE-FREE RECTANGULAR PLATE

Modeling and vibration control of a flexible solar array paddle as a c lamped-free-free-free rectangular plate are considered. This problem h as arisen, in particular, in the area of control of satellites and spa ce stations that have solar array paddles. We consider a flexible plat e in zero gravitational field and rotated about two of its axes by two motors. We first derive a partial differential equation and a set of boundary conditions that represent vibration of the flexible plate, an d ordinary differential equations that represent the dynamics of the a ngles of rotation of the motors. Solving the related eigenvalue proble m, the eigenvalues and the corresponding eigenfunctions are obtained. On the basis of a finite-dimensional modal model of the distributed-pa rameter system, an optimal controller with low-pass property and a rob ust H-infinity controller for the flexible plate are constructed. Simu lations and experiments have been carried out.