On modelling of segmented mirrors mounted on flexible supporting structures

The main goals of this research are to formulate a frequency-matching problem as an exact inverse eigenvalue problem for Jacobi matrices, obtain a state-space representation of the mirror/cell structure, and design decentralized controllers for the push-pull mirror actuators. The interconnected mass-spring model used provides an exact match to the frequency distribution of the mirror/cell structure, and the algorithm does not involve any trial and error procedure. Preliminary results indicate that the model exhibits a decentralized structural characterization, which can be exploited to design local controllers for next-neighbor disturbance rejection.<>