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 clamped-free-free-free rectangular plate are considered. This problem has arisen, in particular, in the area of control of satellites and space stations that have solar array paddles. We consider a flexible plate 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, and ordinary differential equations that represent the dynamics of the angles of rotation of the motors. Solving the related eigenvalue problem, the eigenvalues and the corresponding eigenfunctions are obtained. On the basis of a finite-dimensional modal model of the distributed-parameter system, an optimal controller with low-pass property and a robust H∞ controller for the flexible plate are constructed. Simulations and experiments have been carried out.