Optimal control of large space structures using distributed gyricity

Abstract

An optimal formulation is developed for the shape control of large flexible spacecraft possessing a distribution of control moment gyros. The structure is modeled as a continuum in mass, stiffness, and gyricity (stored angular momentum). A small, linear viscous damping term completes the dynamical description. The equation of motion is formulated in continuum form, and a brief eigenanalysis is presented that permits the modal equations of motion to be derived. The optimal control problem is treated using distributed-parameter concepts, and a modal expansion for the resulting Riccati operator reduces the problem to the solution of a matrix Riccati equation. Such an approach permits pointwise control moment gyros as well as the distributed analog to be handled with the same theory. By means of an example, the use of distributed gyricity is demonstrated to be very effective for shape control of large space structures. Moreover, the notion of a continuous distribution of gyricity is shown to be beneficial in modeling the dynamics and control of flexible spacecraft employing many control moment gyros.