Modal Control of Certain Flexible Dynamic Systems

Interest has increased in the active control of vibrations in mechanically flexible systems, e.g. attitude control of flexible spacecraft, ride quality improvement of air and surface transportation, and active optics. To insure satisfactory performance of such systems, their distributed parameter nature must be taken into account in control system design. In this paper, we obtain feedback control of N nodes of a flexible system and treat the problem of control “spillover” into the uncontrolled modes.We consider the class of flexible systems that can be described by a generalized wave equation, $u_{tt} + Au = F$, which relates the displacement $u(x,t)$ of a body $\Omega $ in n-dimensional space to the applied control forces $F(x,t)$. The operator A is a time-invariant, symmetric differential operator with a discrete semibounded spectrum and the control forces $F(x,t) = \sum_{i = 1}^M {b_i (x)f_i (t)} $ are provided by M actuators with influence functions $b_i (x)$. The displacements are measured by P senso...