Robust control of flexible mechanical system by utilizing symmetry and its application to large space structures

The control issues of the flexible mechanical systems have been extensively studied in a variety of fields. For the mechanical systems with collocated sensors and actuators, it is known to be effective to use a symmetric controller. The symmetric controller guarantees robust stability of the closed loop system, independently from the system parameters, by virtue of the structure of the dynamical equation having positive definite or positive semi definite symmetric coefficient matrices. Although the controller has the advantage over the existing parametric approaches, almost all research works have been concentrated to the stability analysis without discussing the synthesis problems. This paper proposes an optimal design method of the symmetric controller in the sense of H_∞ norm, by solving the linear matrix inequalities reduced from the bounded real lemma. Finally, we apply the design method to a flexible spacecraft mathematical model and its validity is confirmed.