Robust Modal Control of Distributed-Parameter Systems with Uncertainty

Control is designed for decreasing vibratory motion of large flexible structures which possess unknown mass and stiffness distributions, and have disturbance forces acting upon them. A postulated model of a self-adjoint positive definite distributed-parameter system is employed to obtain an orthonormal set of eigenfunctions used to convert the uncertain flexible structure into modal space. A class of robust controls that guarantee practical stability for dynamic systems which consist of interconnected subsystems with uncertainties are then employed to control each mode of the flexible structure. This control is designed based on the possible bound of the uncertainty. Since, it may be difficult to obtain the bound of uncertainty an adaptive algorithm is employed to estimate the bound on-line.