Space Station Freedom solar array H∞ control

Solar array control of the Space Station Freedom is formulated within the framework of the standard H_∞ control problem in an attempt to account for plant model uncertainties. The overriding concern for this type of design is finding a low-order controller that meets the performance criteria. A stepwise approach for deriving an implementable controller that includes only the essential flexible modes in addition to the rigid body modes of the plant, consistent with the performance objectives, is suggested. The overall design procedure relies on the solution of two Riccati equations. Because the plant´s flexible modes have very low damping, poles and zeros of the model are located very close to the imaginary axis. This feature of the system implies that the Riccati equations will be ill-conditioned and that the usual solution methods may fail to compute a usable controller. One of the principal theoretical thrusts of this study is to examine effective numerical techniques to solve such ill-conditioned Riccati (and Lyapunov) equations. In addition to Schur techniques with iterative improvement, the application of matrix-sign-function-based methods has been considered