H₂ energy estimate of boundary controlled vibrating hybrid structure subject to uncertain forces

Abstract

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 H₂ energy estimate of vibrations over a time interval [0,T] in terms of initial energy of the system and the time integral of the L₂ 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.