H_2 Energy Estimate of Boundary Controlled Vibrating Hybrid Structure Subject to Uncertain Forces

摘要

We study here a model hybrid system consisting of a flexible rectangular space structure such as a solar cell array, hoisted at one end by a movable rigid hub, set to vibration from certain initial conditions, but subject to uncertain disturbing forces distributed along its length. Assuming that the control of vibrations is sought by a damper at the hub end proportional to a general nonlinear function of the velocity of the point, we obtain an H_2 energy estimate of vibrations over a time interval [0,T] in terms of initial energy of the system and the time integral of the L_2 norm of the disturbance over the length of the panel. From this, estimates of tolerance level of the disturbances are obtained. Both torsional and flexural modes of vibration are considered.